Question

Find an equation equivalent to r = 10 sin in rectangular coordinates

Answer 1

x²+(y-5)²=25

Explanation:

To convert polar into rectagular

`->r=√(x^2+y^2) =>r^2=x^2+y^2\\`

also, y=rsin θ => sin θ=y/r

r= 10sinθ

r=
`(10y)/(r)` => r²=10y

therefore, x²+y²-10y=0

By completing the squares on y²-10y gives

x²+(y-5)²=25

which is the equation of the circle.

This is the Cartesian equation of a circle with center ( 0, 5)

and radius, r=5