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Flashcards: Expressing Geometric Properties with Equations

What is the equation of the circle shown below?
Plot1

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$

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

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$

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Flashcards: Expressing Geometric Properties with Equations

What is the equation of the circle shown below?
Plot1

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$

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

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$

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Flashcards: Expressing Geometric Properties with Equations

What is the equation of the circle shown below?
Plot1

Your answer:

$\left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$

Your answer:

$\left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$ $\displaystyle \left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$

Your answer:

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

Your answer:

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$

Correct answer:

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot1

we can see that the center is at

$\left ( -7, -2\right )$ $\displaystyle \left ( -7, -2\right )$

The next step it to find the radius. Recall the radius is the distance from the center of the circle to any point on the edge of the circle.

From looking at the picture, we can see that the radius is 4. With this information, we can plug it into the general circle equation

The general circle equation is,

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$ $\displaystyle \left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ $\displaystyle \uptext{a}$ , $\uptext{b}$ $\displaystyle \uptext{b}$ , and $\uptext{c}$ $\displaystyle \uptext{c}$ . When we plug in the values, we get

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$ $\displaystyle \left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

Flashcards: Expressing Geometric Properties with Equations

What is the equation of the circle shown below?
Plot2

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 6$ $\displaystyle \left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 6$

$\left(x - 9\right)^{2} + \left(y + 5\right)^{2} = 36$ $\displaystyle \left(x - 9\right)^{2} + \left(y + 5\right)^{2} = 36$

$\left(x - 9\right)^{2} + \left(y - 5\right)^{2} = 36$ $\displaystyle \left(x - 9\right)^{2} + \left(y - 5\right)^{2} = 36$

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$ $\displaystyle \left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

$\left(x + 9\right)^{2} + \left(y - 5\right)^{2} = 6$ $\displaystyle \left(x + 9\right)^{2} + \left(y - 5\right)^{2} = 6$

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Flashcards: Expressing Geometric Properties with Equations

What is the equation of the circle shown below?
Plot2

Your answer:

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 6$ $\displaystyle \left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 6$

Your answer:

$\left(x - 9\right)^{2} + \left(y + 5\right)^{2} = 36$ $\displaystyle \left(x - 9\right)^{2} + \left(y + 5\right)^{2} = 36$

Your answer:

$\left(x - 9\right)^{2} + \left(y - 5\right)^{2} = 36$ $\displaystyle \left(x - 9\right)^{2} + \left(y - 5\right)^{2} = 36$

Your answer:

$\left(x + 9\right)^{2} + \left(y - 5\right)^{2} = 6$ $\displaystyle \left(x + 9\right)^{2} + \left(y - 5\right)^{2} = 6$

Correct answer:

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$ $\displaystyle \left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot2

we can see that the center is at $\left ( -9, -5\right )$ $\displaystyle \left ( -9, -5\right )$ .

The next step it to find the radius. Recall the radius is the distance from the center of the circle to any point of the circle's edge.

From looking at the picture, we can see that the radius is 6.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$ $\displaystyle \left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ $\displaystyle \uptext{a}$ , $\uptext{b}$ $\displaystyle \uptext{b}$ , and $\uptext{c}$ $\displaystyle \uptext{c}$ .

When we plug in the values, we get

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$ $\displaystyle \left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

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Flashcards: Expressing Geometric Properties with Equations

All Common Core: High School - Geometry Resources

Flashcards: Expressing Geometric Properties with Equations

Flashcards: Expressing Geometric Properties with Equations

Flashcards: Expressing Geometric Properties with Equations

Flashcards: Expressing Geometric Properties with Equations

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