Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 10 - Conics, Parametric Equations, and Polar Coordinates - 10.4 Exercises - Page 722: 42

Answer

Rectangular equation: $y^2 - x = 0$ Graph:

Work Step by Step

**Remember:(I) $r^2 = x^2 + y^2$, (II) $tan(θ) = \frac{y}{x}$, (III) $rcos(θ) = x$, (IV) $rsin(θ) = y$ $r = cot(θ)csc(θ)$ $r = \frac{1}{tan(θ)sin(θ)}$ Multiplying both sides by "tan(θ)sin(θ)": $rtan(θ)sin(θ) = 1$ Using (IV) and (II): $y\frac{y}{x} = 1$ $\frac{y^2}{x}= 1$ Multiplying both sides by "x": $y^2 = x$ $y^2 - x = 0$
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