Find a polar equation for the curve represented by the given cartesian equation. x² + y² = 8cx

Solution:

The Cartesian equation given is

x² + y² = 8cx

The relation between polar and cartesian coordinates are

x = r cosθ

y = r sinθ

Where r is the radius and θ is the angle

By replacing these relations in the given cartesian equation

(r cosθ)² + (r sinθ)² = 8c (r cos θ)

It can be written as

r² cos² θ + r² sin² θ = 8cr cosθ

r² (cos² θ + sin² θ) = 8cr cosθ

Using the trigonometric identity cos² θ + sin² θ = 1

r² = 8cr cosθ

r = 8c cosθ

Therefore, the polar equation is r = 8c cosθ.

Find a polar equation for the curve represented by the given cartesian equation. x² + y² = 8cx

Summary:

The polar equation for the curve represented by the given Cartesian equation x² + y² = 8cx is r = 8c cosθ.