All SSAT Upper Level Math Resources
Example Questions
Example Question #1 : Circles
Give the equation of the above circle.
None of the other choices is correct.
A circle with center and radius
has equation
The circle has center and radius 5, so substitute:
Example Question #2 : How To Find The Equation Of A Circle
A circle on the coordinate plane has a diameter whose endpoints are and
. Give its equation.
A circle with center and radius
has equation
The midpoint of a diameter of the circle is its center, so use the midpoint formula to find this:
Therefore, and
The radus is the distance between the center and one endpoint, so take advantage of the distance formula using and
. We will concern ourcelves with finding the square of the radius
:
Substitute:
Example Question #3 : How To Find The Equation Of A Circle
Give the equation of the above circle.
A circle with center and radius
has equation
The circle has center and radius 4, so substitute:
Example Question #4 : How To Find The Equation Of A Circle
A circle on the coordinate plane has a diameter whose endpoints are and
. Give its equation.
A circle with center and radius
has equation
The midpoint of a diameter of the circle is its center, so use the midpoint formula to find this:
Therefore, and
.
The radus is the distance between the center and one endpoint, so take advantage of the distance formula using and
. We will concern ourcelves with finding the square of the radius
:
Substitute:
Expand:
Example Question #1 : How To Find The Equation Of A Circle
A circle on the coordinate plane has center and circumference
. Give its equation.
A circle with center and radius
has equation
The center is , so
.
To find , use the circumference formula:
Substitute:
Example Question #6 : How To Find The Equation Of A Circle
A circle on the coordinate plane has center and area
. Give its equation.
A circle with center and radius
has the equation
The center is , so
.
The area is , so to find
, use the area formula:
The equation of the line is therefore:
Example Question #7 : How To Find The Equation Of A Circle
What is the equation of a circle that has its center at and has a radius of
?
The general equation of a circle with center and radius
is:
Now, plug in the values given by the question:
Example Question #8 : How To Find The Equation Of A Circle
If the center of a circle with a diameter of 5 is located at , what is the equation of the circle?
Write the formula for the equation of a circle with a given point, .
The radius of the circle is half the diameter, or .
Substitute all the values into the formula and simplify.
Example Question #9 : How To Find The Equation Of A Circle
Give the circumference of the circle on the coordinate plane whose equation is
The standard form of the equation of a circle is
where is the radius of the circle.
We can rewrite the equation we are given, which is in general form, in this standard form as follows:
Complete the squares. Since and
, we do this as follows:
, so
, and the circumference of the circle is
Example Question #10 : How To Find The Equation Of A Circle
A square on the coordinate plane has as its vertices the points . Give the equation of a circle circumscribed about the square.
Below is the figure with the circle and square in question:
The center of the inscribed circle coincides with that of the square, which is the point . Its diameter is the length of a diagonal of the square, which is
times the sidelength 6 of the square - this is
. Its radius is, consequently, half this, or
. Therefore, in the standard form of the equation,
,
substitute and
.
All SSAT Upper Level Math Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)