   Chapter 10.5, Problem 77E

Chapter
Section
Textbook Problem

# Conic What conic section does the polar equation r = a sin θ + b cos θ represent?

To determine

The conic represented by the polar equation r=asinθ+bcosθ.

Explanation

Consider the given equation of polar curve, r=asinθ+bcosθ.

Convert the equation in any standard form of the conic.

Multiply both sides of the equation by r.

r(r)=r(asinθ+bcosθ)r2=rasinθ+rbcosθ=arsinθ+brcosθ=a(rsinθ)+b(rcosθ)

Use the following conversions.

For converting polar to rectangular coordinate system,

x=rcosθy=rsinθ

For converting rectangular to polar coordinate system,

tanθ=yxr2=x2+

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