Question

Write the rectangular equation (x + 5)2 + y2 = 25 in polar form.

A)r= -10sin 0

B)r=5

C)r= 5 cos 0

D)r=-10cos 0

Answer 1

r = -10costheta

Explanation:

Given the rectangular equation

(x + 5)² + y² = 25

in polar coordinate

x = rcos theta

y = rsin theta

Substitute into the expression

(rcos theta + 5)²+(rsin theta)² = 25

r²cos²theta + 10rcos theta +25 +r²sin²theta = 25

r²cos²theta+r²sin²theta+ 10rcos theta= 0

r²(cos²theta+sin²theta) + 10rcostheta = 0

r² + 10rcostheta = 0

r² = -10rcostheta

r = -10costheta

Hence the correct option is D