Question 1

Which of the following polar equations best matches the graph shown in Image 1 (the first image with multiple petals)?

Accepted Answer

$$r = 4 \sin(4	heta)$$

Question 2

Given the ellipse shown in Image 2 (centered at $$(-2, 3)$$), which of the following is the correct standard form equation for this ellipse?

Accepted Answer

$$\frac{(x+2)^2$}{36} + \frac{(y-3)^2$}{9} = 1$$

Question 3

Which of the following graphs (Images 3 or 4) best represents the ellipse with equation $$\frac{(x+2)^2$}{4} + \frac{(y-1)^2$}{9} = 1$$?

Accepted Answer

Image 4

Question 4

For the ellipse in Image 2, what are the coordinates of its foci?

Accepted Answer

$$(-2 + 3\sqrt{3}, 3)$$ and $$(-2 - 3\sqrt{3}, 3)$$

Question 5

Which of the following best describes the symmetry of the graph in Image 1?

Accepted Answer

It is symmetric about the x-axis, y-axis, and the origin.

Question 6

If the equation of an ellipse is $$\frac{(x+2)^2$}{4} + \frac{(y-1)^2$}{9} = 1$$, what are the lengths of the major and minor axes?

Accepted Answer

Major axis: 6, Minor axis: 4

Question 7

Which of the following is the correct rectangular equation for the polar equation $$r = 4 \sin(4	heta)$$?

Accepted Answer

This equation cannot be easily converted to a simple rectangular form.

Question 8

Given the ellipse in Image 4, what is the center of the ellipse?

Accepted Answer

$$(-2, 1)$$

Question 9

Which of the following statements is true about the graph in Image 1?

Accepted Answer

It has 8 petals, each symmetric about the origin.

Question 10

For the ellipse in Image 2, what is the length of the major axis?

Accepted Answer

12

Exam 3 Review: Precalculus Study Guidance (Polar and Elliptic Equations)

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