Convert from a polar equation to a rectangular equation?

Question

r=6cos0+4sin0

the zeros are supposed to be the ones with the slash in them.

Answer 1

r=6cost+4sint

r^2 = 6rcost+ 4rsint x=rcost, y=rsint, r^2=x^2+y^2

x^2+y^2 = 6x+4y

x^2-6x+9 + y^2 -4y +4 = 9+4 = 13

(x-3)^2 + (y-2)^2 = 13

It's a circle with center (3,2) radius = sqr13

Answer 2

r = 6cosθ + 4sinθ;

Let multiply this equation by r: r² = 6rcosθ + 4rsinθ; or x² + y² = 6x + 4y;

We complete squares: (x - 3)² + (y - 2)² = 13.

This is circle with center (3, 2) and radius r = √13