Question

Which of the following parametric equations are equivalent to the polar equation r=3 cos theta

Answer 1

B

Explanation:

Answer 2

To solve the problem you must know that to change from Cartesian to polar coordinates you must write:
x = rcos (θ)
Where "r" is the radius
Likewise y = rsin (θ)
Therefore, in the expression r = 3cos (θ) one can write r as:
r = x / cos (θ)
So:
x / cos (θ) = 3cos (θ)
x = 3cos ^ 2 (θ)
The same for y ...
y = rsin (θ)
y = 3cos (θ) sin (θ).

Finally the correct answer is option 2.
x = 3cos ^ 2 (θ) y = 3cos (θ) sin (θ).