Question

Convert the equation r equals negative 14 cosine thetar=−14cosθ to cartesian coordinates. Describe the resulting curve.

Answer 1

Multiply the equation by r to get

... r² = -14·r·cos(θ)

Then make the usual substitutions:

x² +y² = r²

x = r·cos(θ)

This gives

... x² +y² = -14x

... x² +14x +49 +y² = 49 . . . . . add 49+14x

... (x +7)² + y² = 49 . . . . . . . . . equation of circle of radius 7 with center (-7, 0)