Convert each of the following equations from rectangular form to polar form. Solve for r.

Question

a) 𝑦=7

b) (𝑥−3)^2 +𝑦^2 =9

Hello! I am confused about these two problems and I need help solving them, please!

Answer 1

a)

y = rsinθ

r = y/sinθ = 7/sinθ

b)

(x-3)²+y²=9

Expanding

x²-6x+9 + y²=9

Substituting y=rsinθ and x=rcosθ

r²cos²θ-6rcosθ+9 + r²sin²θ = 9

Simplifying

r²(sin²θ+cos²θ) - 6rcosθ=0

r²(1)=6rcosθ

r = 6cosθ

Note: From the original equation, this is a circle with a radius of 3, centered at (3,0).

Probably more obvious by:

(x-3)²/9 + y²/9 = 1