Question

How do you convert `r= -2sin(theta)` into rectangular form?

Answer 1

`x^2+(y+1)^2=1`.
This represents the unit circle through the orifgin, with center at (0, -1).

Explanation:

Use the conversion equation `r(cos theta, sin theta)=(x, y)`.

As `y =r sin theta and r`2=x^2+y^2#,

`r=-2 sin theta =-y/r`. and so,

`r^2=x^2+y^2=-2y`.

In the standard form,

`x^2+(y+1)^2=1`.

This represents the unit circle through the origin with center at (0, -1).

The general polar equation for the family of circles through the

pole r = 0 is

`r = dcos(theta+alpha)` that has center at #(d/2 cos alpha, d/2sin

alpha)#. |d| is the diameter.

The rectangular form is

`(x+d/2cos alpha)^2+(y+d/2sin alpha)^2=d^2/4`

Here, `d = -2 and alpha = -pi/2`.. .