Use the relationships x = r cos Ø and y= r sin Ø to write the equation r = (4)/(1- cos Ø) in terms of x and y

Answer 1

r = (4)/(1 - cos(Ø))

Multiply both sides by (1 - cos(Ø)),

r(1 - cos(Ø)) = 4

r - rcos(Ø) = 4

But r = sqrt(x^2 + y^2), and rcos(Ø) = x, so

sqrt(x^2 + y^2) - x = 4
sqrt(x^2 + y^2) = x + 4
x^2 + y^2 = x^2 + 8x + 16
y^2 = 8x + 16, which is a sideways parabola.

Answer 2

plugging in we get (r cos Ø)^2 - (r sin Ø)^2 = a million in terms of r and Ø. r^2 [(cos Ø)^2 - (sin Ø)^2] =a million the respond above satisfies the standards yet you may simplify extra by using using the sin^2+cos^2=a million identity to get: r^2 [(cos Ø)^2 -(a million- cos Ø)^2] =a million r^2 [2(cos Ø)^2 -a million] =a million is the least perplexing sort

Answer 3

r = (4)/(1- cos Ø)
r^2 = 16/(1 - cosØ)^2
x^2+y^2 = 16(1- x/sqrt(x^2+y^2))^2