Which of the following is not a polar equation of a conic?

Question

asked Jul 16, 2020 45.1k views

2 Answers

Gnqz · Answer 1 · 2020-07-22T16:52:19+0000

Answer:

a.
$r=1+2\cos(\theta)$

Explanation:

The curve

$r=1+2\cos(\theta)$

is not a conic.

Convert to rectangular coordinates.

First multiply through by r.

$r^2=r+2r\cos(\theta)$

Substitute
r^2=x^2+y^2

and

$x=r\cos(\theta)$

x^2+y^2=√(x^2+y^2)+2x

We can see clearly that this is not a conic.

$r=1+2\cos(\theta)$ is an equation of a cardioid.

r=3 is a circle.

$r=(1)/(1+\sin(\theta))$ is a parabola.

$r=(1)/(2-\cos(\theta))$ is an ellipse.