Question

Find a Cartesian equation for the curve? r = 5 sin(θ)

Answer 1

`x^2+y^2-5y=0`

Explanation:

`"to convert from "color(blue)"polar to cartesian form"`

`•color(white)(r)r=sqrt(x^2+y^2)`

`•color(white)(x)y=rsinthetarArrsintheta=y/r`

`r=5sintheta`

`rArrr=5xxy/r`

`"multiply both sides by r"`

`rArrr^2=5y`

`rArrx^2+y^2-5y=0`

`"which is the equation of a circle"`

`"centre "=(0,5/2)" and radius "r=5/2`
graph{x^2+y^2-5y=0 [-10, 10, -5, 5]}