QUICK HELP??????

Question

Rewrite the following equation and polar form x^2+(y-5)^2=25

show work .your final answer should be r=

Answer 1

x²+(y-5)²=25

(r·cosθ)² + (r·sinθ - 5)² = 25 <-- Recall x=r·cosθ and y=r·sinθ

r²cos²θ + r²sin²θ - 10rsinθ + 25 = 25

r²(cos²θ + sin²θ) - 10r·sinθ = 0

r² - 10r·sinθ = 0 <-- Pythagorean Identity

r² = 10r·sinθ

r = 10sinθ

Hope this helped!

Answer 2

The given equation is:

x^2 + (y-5)^2 = 25

We can rewrite this equation in polar coordinates by substituting x with r cosθ and y with r sinθ:

(r cosθ)^2 + (r sinθ - 5)^2 = 25

Simplifying this equation:

r^2 cos^2θ + r^2 sin^2θ - 10r sinθ + 25 = 25

r^2 cos^2θ + r^2 sin^2θ = 10r sinθ

Using the identity cos^2θ + sin^2θ = 1, we can simplify this equation further:

r^2 = 10r sinθ

Dividing both sides by r:

r = 10 sinθ

Therefore, the polar form of the equation x^2 + (y-5)^2 = 25 is r = 10 sinθ.