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# Find a polar equation for the curve represented by the given cartesian equation. x^{2} + y^{2} = 8cx

**Solution:**

The Cartesian equation given is

x^{2} + y^{2} = 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

r^{2} cos^{2} θ + r^{2} sin^{2} θ = 8cr cosθ

r^{2} (cos^{2} θ + sin^{2} θ) = 8cr cosθ

Using the trigonometric identity cos^{2} θ + sin^{2} θ = 1

r^{2} = 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. x^{2} + y^{2} = 8cx

**Summary:**

The polar equation for the curve represented by the given Cartesian equation x^{2} + y^{2} = 8cx is r = 8c cosθ.

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