Answer:
r = -10costheta
Step-by-step 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
