Rectangular coordinates, identify curve

Question

rewrite the equation r = 10 cos θ in rectangular coordinates and identify the curve in words

Answer 1

The identities you use are:

1) cos(θ) = x/r meaning that x = rcos(θ)

2) sin(θ) = y/r meaning that y = rsin(θ)

3) x² + y² = r²

Starting with r = 10cos(θ)

Replace cos(θ) with "x/r" from identity #1 to get: r = 10(x/r)

Multiply both sides by "r" to get: r² = 10x

Replace r² with "x² + y²" from identity #3 to get: x² + y² = 10x

x² - 10x + y² = 0

x² - 10x + 25 + y² = 25

(x - 5)² + y² = 25

This is the standard form for a circle of radius 5 with the center at (5, 0)