# SAT II Math I : Parabolas and Circles

## Example Questions

### Example Question #1 : Parabolas And Circles

Give the axis of symmetry of the parabola of the equation

Explanation:

The line of symmetry of the parabola of the equation

is the vertical line

Substitute :

The line of symmetry is

That is, the line of the equation .

### Example Question #1 : Parabolas And Circles

What is the center of the circle with the following equation?

Explanation:

Remember that the basic form of the equation of a circle is:

This means that the center point  is defined by the two values subtracted in the squared terms.  We could rewrite our equation as:

Therefore, the center is

### Example Question #1 : Coordinate Geometry

What is the area of the sector of the circle formed between the -axis and the point on the circle found at  when the equation of the circle is as follows?

Round your answer to the nearest hundreth.

Explanation:

For this question, we will need to do three things:

1. Determine the point in question.
2. Use trigonometry to find the area of the angle in question.
3. Use the equation for finding a sector area to finalize our answer.

Let us first solve for the coordinate by substituting into our equation:

Our point is, therefore:

Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of  to  is here:

Therefore, the angle is:

To solve for the sector area, we merely need to use our standard geometry equation. Note that the radius of the circle, based on the equation, is .

This rounds to .

### Example Question #1 : Parabolas And Circles

What is the area of the sector of the circle formed between the -axis and the point on the circle found at  when the equation of the circle is as follows?

Round your answer to the nearest hundreth.

Explanation:

For this question, we will need to do three things:

1. Determine the point in question.
2. Use trigonometry to find the area of the angle in question.
3. Use the equation for finding a sector area to finalize our answer.

Let us first solve for the coordinate by substituting into our equation:

Our point is, therefore:

Now, we need to calculate the angle formed between the origin and the point that we were given. We can do this using the inverse tangent function. The ratio of  to  is here:

Therefore, the angle is:

To solve for the sector area, we merely need to use our standard geometry equation. Note that , based on the equation, is .

This rounds to .

### Example Question #1 : Parabolas And Circles

If the center of a circle is at  and it has a radius of , what positive point on the  does it intersect?