# Convert the polar equation to the Cartesian equation

## Homework Statement

Replace the polar equation with an equivalent Cartesian equation.

$r^2 = 26r cos θ - 6r sin θ - 9$
a)$(x - 13)^2 + (y + 3)^2 = 9$
b)$(x + 26)^2 + (y - 6)^2 = 9$
c)$26x - 6y = 9$
d)$(x - 13)^2 + (y + 3)^2 = 169$

## Homework Equations

$x= r cos \theta$
$y= r sin \theta$
$x^2+y^2 = r^2$

## The Attempt at a Solution

$r^2 = 26r cos θ - 6r sin θ - 9$
$x^2 + y^2 = 26 x - 6 y -9$
$x^2 -26x + y^2 + 6 y = -9$
$(x-13)^2 - 169 + ( y+3 )^2 -9 = -9$
$(x-13)^2 + (y+3)^2 = 169$
The answer is (d) . Right ?