# SSAT Upper Level Math : Circles

## Example Questions

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### Example Question #1 : How To Find The Equation Of A Circle

Give the equation of the above circle.

None of the other choices is correct.

Explanation:

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.

Explanation:

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.

Explanation:

A circle with center  and radius  has equation

The circle has center  and radius 4, so substitute:

### Example Question #251 : Coordinate Geometry

A circle on the coordinate plane has a diameter whose endpoints are  and . Give its equation.

Explanation:

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 #252 : Coordinate Geometry

A circle on the coordinate plane has center  and circumference . Give its equation.

Explanation:

A circle with center  and radius  has equation

The center is , so .

To find , use the circumference formula:

Substitute:

### Example Question #253 : Coordinate Geometry

A circle on the coordinate plane has center  and area . Give its equation.

Explanation:

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 #254 : Coordinate Geometry

What is the equation of a circle that has its center at  and has a radius of ?

Explanation:

The general equation of a circle with center  and radius  is:

Now, plug in the values given by the question:

### Example Question #255 : Coordinate Geometry

If the center of a circle with a diameter of 5 is located at , what is the equation of the circle?

Explanation:

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 #256 : Coordinate Geometry

Give the circumference of the circle on the coordinate plane whose equation is

Explanation:

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 #257 : Coordinate Geometry

A square on the coordinate plane has as its vertices the points . Give the equation of a circle circumscribed about the square.