Question

What type of limacon is graphed by the polar equation r=4+2 sin theta? Identify the axis of symmetry and horizontal and vertical intercepts.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The type of limacon graphed by the polar equation r = 4 + 2sin(theta) is a cardioid. The axis of symmetry is the polar axis (theta = 0) and the polar axis (theta = pi) since the equation is symmetrical around these angles.

To find the horizontal and vertical intercepts, we need to set r equal to zero:

0 = 4 + 2sin(theta)
-2 = sin(theta)

Since sine can only take values between -1 and 1, there are no solutions for theta that satisfy this equation. Therefore, there are no horizontal or vertical intercepts for this particular polar equation.