The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 9\right)^{2} = 1$

$\displaystyle \left ( k, h\right )$ is the coordinates of the center of the foci.

$\displaystyle {a}$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii is $\displaystyle a$.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 10$

Now solve for $\displaystyle a$

$\displaystyle a = 5.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = 2 \\y = 3.0$

So the center of the foci is at $\displaystyle \left ( 2, 3\right )$.

Now we need to figure out what the distance from the center to the foci is $\displaystyle c$.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = -7$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 5.0 and $\displaystyle c$ with -7

$\displaystyle b^{2} = -24.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{25} \left(x - 2\right)^{2} - \frac{1}{24} \left(y - 3\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 7\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii is $\displaystyle a$.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 18$

Now solve for $\displaystyle a$.

$\displaystyle a = 9.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = 0 \\y = 1.0$

So the center of the foci is at $\displaystyle \left ( 0, \quad 1\right )$

Now we need to figure out what the distance from the center to the foci is $\displaystyle c$.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = -7$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 9.0 and $\displaystyle c$ with -7

$\displaystyle b^{2} = 32.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{x^{2}}{81} + \frac{1}{32} \left(y - 1\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 3\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii $\displaystyle a$ is.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 18$

Now solve for $\displaystyle a$

$\displaystyle a = 9.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = -1 \\y = 4.0$

So the center of the foci is at $\displaystyle \left ( -1, \quad 4\right )$

Now we need to figure out what the distance from the center to the foci $\displaystyle c$ is.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = -4$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 9.0 and $\displaystyle c$ with -4

$\displaystyle b^{2} = 65.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{81} \left(x + 1\right)^{2} + \frac{1}{65} \left(y - 4\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x + 3\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii $\displaystyle a$ is.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 16$

Now solve for $\displaystyle a$

$\displaystyle a = 8.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = -2 \\ y = 5.0$

So the center of the foci is at $\displaystyle \left ( -2, \quad 5\right )$

Now we need to figure out what the distance from the center to the foci is $\displaystyle c$.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate.

$\displaystyle c = 1$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 8.0 and $\displaystyle c$ with 1

$\displaystyle b^{2} = 63.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{64} \left(x + 2\right)^{2} + \frac{1}{63} \left(y - 5\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 4\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii $\displaystyle a$ is.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 2$

Now solve for $\displaystyle a$

$\displaystyle a = 1.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = 1 \\y = -10.0$

So the center of the foci is at$\displaystyle \left ( 1, \quad -10\right )$

Now we need to figure out the distance from the center to the foci $\displaystyle c$.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = -3$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 1.0 and $\displaystyle c$ with -3.

$\displaystyle b^{2} = -8.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \left(x - 1\right)^{2} - \frac{1}{8} \left(y + 10\right)^{2} = 1$

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 5\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii $\displaystyle a$ is.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 18$

Now solve for $\displaystyle a$

$\displaystyle a = 9.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = \frac{15}{2} \\\\ y = 6.0$

So the center of the foci is at $\displaystyle \left ( \frac{15}{2}, \quad 6\right )$

Now we need to figure out what the distance from the center to where the foci $\displaystyle c$ is.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = \frac{5}{2}$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 9.0 and $\displaystyle c$ with $\displaystyle \frac{5}{2}$

$\displaystyle b^{2} = 74.75$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{81} \left(x - \frac{15}{2}\right)^{2} + \frac{4}{299} \left(y - 6\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x + 10\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii $\displaystyle a$ is.

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 12$

Now solve for $\displaystyle a$

$\displaystyle a = 6.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = -3 \\y = -10.0$

So the center of the foci is at $\displaystyle \left ( -3, \quad -10\right )$

Now we need to figure out what the distance from the center to the foci $\displaystyle c$ is.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = 7$
Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 6.0 and $\displaystyle c$ with 7

$\displaystyle b^{2} = -13.0$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{36} \left(x + 3\right)^{2} - \frac{1}{13} \left(y + 10\right)^{2} = 1$ 

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 5\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii is ($\displaystyle a$).

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 14$

Now solve for $\displaystyle a$

$\displaystyle a = 7.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = - \frac{1}{2} \\\\y = -1.0$

So the center of the foci is at $\displaystyle \left ( - \frac{1}{2}, \quad -1\right )$

Now we need to figure out what the distance from the center to the foci $\displaystyle c$.

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = - \frac{11}{2}$

Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 7.0 and $\displaystyle c$ with $\displaystyle - \frac{11}{2}$

$\displaystyle b^{2} = 18.75$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{49} \left(x + \frac{1}{2}\right)^{2} + \frac{4}{75} \left(y + 1\right)^{2} = 1$

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x + 8\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii is ($\displaystyle a$).

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 18$

Now solve for $\displaystyle a$

$\displaystyle a = 9.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = - \frac{5}{2} \\\\y = -5.0$

So the center of the foci is at $\displaystyle \left ( - \frac{5}{2}, \quad -5\right )$

Now we need to figure out what the distance from the center to the foci is ($\displaystyle c$).

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = \frac{11}{2}$
Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 9.0 and $\displaystyle c$ with $\displaystyle \frac{11}{2}$

$\displaystyle b^{2} = 50.75$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{81} \left(x + \frac{5}{2}\right)^{2} + \frac{4}{203} \left(y + 5\right)^{2} = 1$

The general equation is

$\displaystyle \frac{1}{b^{2}} \left(- h + y\right)^{2} + \frac{1}{a^{2}} \left(x - 7\right)^{2} = 1$

$\displaystyle \left ( k, \quad h\right )$ is the coordinates of the center of the foci.

$\displaystyle a$ is the distance to the foci on the x-axis from the center, and $\displaystyle b$ is the distance to the foci from the y-axis.

The first step is to figure out what the focal radii is ($\displaystyle \uptext{a}$).

Since we know the distance of the major axis, all we need to do is set up a simple equation.

$\displaystyle 2 a = 16$

Now solve for $\displaystyle a$

$\displaystyle a = 8.0$

The next step is to find the center between the foci.

To find the center, we simply find the average between the coordinates.

$\displaystyle \\x = \frac{7}{2} \\\\y = -1.0$

So the center of the foci is at $\displaystyle \left ( \frac{7}{2}, \quad -1\right )$

Now we need to figure out what the distance from the center to the foci is ($\displaystyle \uptext{c}$).

We do this by taking the x-coordinate from one of the foci and subtracting it from the center x-coordinate

$\displaystyle c = - \frac{7}{2}$
Now the last part is to find $\displaystyle b$.

We can find it by using the following equation.

$\displaystyle b^{2} = a^{2} - c^{2}$

We simply substitute $\displaystyle a$ with 8.0 and $\displaystyle c$ with $\displaystyle - \frac{7}{2}$

$\displaystyle b^{2} = 51.75$

Now we can substitute these values into the general equation to get.

$\displaystyle \frac{1}{64} \left(x - \frac{7}{2}\right)^{2} + \frac{4}{207} \left(y + 1\right)^{2} = 1$