Converting Polar Equations

Question

Given x^2 - y^2 = 9, find what r^2 equals. (Covert from Cartesian to Polar). I am pretty confused on how to solve this, so if you could go step-by-step, it would be greatly appreciated!

Answer 1

x^2 + y^2 = r^2 =9

r^2 = 9

r =3 is the equation in polar form for a circle with center at the origin and radius = 3

x^2 +y^2 = 9

is a circle with center at the origin and radius =sqr9 = 3

the conversion equations are

r^2 = x^2 + y^2

rcos(theta) = x

rsin(theta) = y

x^2 + y^2 = (rcos(theta))^2 + (rsin(theta))^2 = r^2cos^2(theta) + r^2sin^2(theta)

= r^2(cos^2(theta) + sin^2(theta)) = r^2(1) = r^2

in this specific example theta is any angle and r is only =3

in rectangular coordinates (x-h)^2 + (y-k)^2 = r^2 is a circle with center at (h,k) and radius = r

for x^2 +y^2 =9 the center is (0,0) = (h,k) and r = sqr9 = 3