Find a cartesian equation for the curve. r = 10 sin(θ) + 10 cos(θ)

Solution:

Given r = 10 sin(θ) + 10 cos(θ)-----(1)

Let x = r cos θ; y = r sin θ such that x² + y² = r²

Now multiply both sides of equation (1) by r,

⇒ r² = 10(r cos θ) + 10 (r sin θ)

⇒ x² + y² = 10[(r cos θ) + (r sin θ)]

⇒ x² + y² = 10 (x + y) 

⇒ x² + y² - 10x - 10y = 0

This is the required cartesian equation.

Find a cartesian equation for the curve. r = 10 sin(θ) + 10 cos(θ)

Summary:

The cartesian equation for the curve r = 10 sin(θ) + 10 cos(θ) is x² + y² - 10x - 10y = 0.