Answer
$3x^2+4y^2-12x-36=0$,
Ellipse.
Work Step by Step
$r=\frac{6sec\theta}{2sec\theta-1}$,
$r=\frac{6}{2-cos\theta}$,
$2r=6+r\ cos\theta$,
$4r^2=(6+r\ cos\theta)^2$,
$4x^2+4y^2=(6+x)^2$,
$3x^2+4y^2-12x-36=0$,
Ellipse.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 9 - Analytic Geometry - Section 9.6 Polar Equations of Conics - 9.6 Assess Your Understanding - Page 704: 35
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