Question

What is the polar equation with the same graph as (x+2)^2 + (y-1)^2 = 5?

Answer 1

`r=2sintheta - 4costheta`

Explanation:

This graph is a circle of radius `sqrt5` centred at `(–2, 1)`.

Converting Cartesian coordinates to polar coordinates:

`x = r cos theta`
`y = r sin theta`

So we get

`(x+2)^2 + (y-1)^2 = 5`

`(r cos theta + 2)^2 + (r sin theta - 1)^2 = 5`

`r^2 cos^2 theta + 4rcostheta+4+r^2sin^2theta-2rsintheta+1=5`

`r^2(cos^2 theta + sin^2theta)+ 4rcostheta+4-2rsintheta+1=5`

`r^2(1)+ 4rcostheta-2rsintheta=0`

`r+ 4costheta-2sintheta=0`

Solving for `r`:

`r = 2sintheta - 4costheta`
graph{(x+2)^2+(y-1)^2=5 [-10.99, 6.78, -3.19, 5.7]}