Question

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

Answer 1

Answer:

x²+(y-5)²=25

Step-by-step explanation:

To convert polar into rectagular

$->r=\sqrt{x^2+y^2} =>r^2=x^2+y^2$

also, y=rsin θ => sin θ=y/r

r= 10sinθ

r=$\frac{10y}{r}$ => 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