Conics and Polar

Identify the polar equation:

r² = 9cos(2θ)

• lemniscate

• limacon with inner loop

• cardioid

• rose

Describe the curve

• Rose with 3 leaves

• Circle

• Cardioid

• Inner loop limacon

Standard Form of a Ellipse

• (x-h)² + (y-k)² = r²

• (x-h)²/a² + (y-k)²/b² = 1

• (x-h)²/a² - (y-k)²/b² = 1

• x = a(y-h)² + k

The major axis is:

• The shorter axis of an ellipse

• The longer axis of an ellipse

• The closest point closest to the Sun

• The farthest point closest to the Sun

What is the center, a and b values for the following equation:
x² + 4y² + 16x - 80y + 320 = 0

• (-8, 10); a = 12, b = 6

• (-8, 10); a = 6, b = 12

• (8, -10); a = 12, b = 6

• (8, -10); a = 6, b = 12

What are the co-vertices of the ellipse?

• (1, 5) and (1, -5)

• (0, 0) and (2, 0)

• (4, 0) and (6, 0)

• (1, 6) and (1, 4)

What are the vertices of the ellipse?

• (0, 0)

• (7, 1) and (-1, 1)

• (3, -5) and (3, 7)

• (3, 1)

In an ellipse, what distance does a represent?

• The distance from the center to a vertex

• The distance from the center to a co-vertex

• The distance from the center to a focus

• The length of the minor axis

• The length of the major axis

In an ellipse, what distance does b represent?

• The distance from the center to a vertex

• The distance from the center to a co-vertex

• The distance from the center to a focus

• The length of the minor axis

• The length of the major axis

In an ellipse, what distance does c represent?

• The distance from the center to a vertex

• The distance from the center to a co-vertex

• The distance from the center to a focus

• The length of the minor axis

• The length of the major axis