### All SSAT Upper Level Math Resources

## Example Questions

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

Give the equation of the above circle.

**Possible Answers:**

None of the other choices is correct.

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

A circle with center and radius has equation

The circle has center and radius 4, so substitute:

### Example Question #3 : How To Find The Equation Of A Circle

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

**Possible Answers:**

**Correct answer:**

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 #4 : How To Find The Equation Of A Circle

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

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 #5 : 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 ?

**Possible Answers:**

**Correct answer:**

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

Now, plug in the values given by the question:

### Example Question #6 : 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?

**Possible Answers:**

**Correct answer:**

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 #6 : How To Find The Equation Of A Circle

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

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 .