Question

Rewrite the following rectangular equation in polar form assuming a is a real constant.x2 + y2 = 11a=

Answer 1

The polar form is

r = √11a

Step-by-step explanation:

The given equation is

x^2 + y^2 = 11a

Recall,

x = rcosθ

y = rsinθ

By substituting these values into the equation, we have

(rcosθ )^2 + ( rsinθ)^2 = 11a

r^2cos^2θ + r^2sin^2θ = 11a

r^2cos^2θ + r^2sin^2θ - 11a = 0

By factorizing r^2, we have

r^2(cos^2θ + sin^2θ) = 11a

Recall, cos^2θ + sin^2θ = 1

Thus, we have

r^2 = 11a

Taking the square root of both sides,

r = √11a

The polar form is

r = √11a