Calculus 10th Edition

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

Chapter P - P.1 - Graphs and Models - Exercises - Page 9: 72

Answer

a) $k=1/4$; b) $k=2$; c) $k$ is any real number; d) $k=4/3$.

Work Step by Step

In all of the parts we substitute for y the second coordinate of the point and for x the first coordinate of the point into the equation $y^2=4kx$ and then we calculate k. a) $$1^2=4k\times 1\Rightarrow 1=4k\Rightarrow k=\frac{1}{4}$$ so for $k=1/4$ the graph passes through $(1,1)$. b) $$4^2 = 4k\times2 \Rightarrow 16=8k\Rightarrow k=\frac{16}{8} = 2$$ so for $k=2$ the graph passes through $(2,4)$. c) $$0^2 = 4k\times 0\Rightarrow 0=k\times 0.$$ The last equation is true for any real value of $k$ so for any $k\in \mathbb{R}$ the graph passes through $(0,0)$. d) $$3^2 = 4k\times3 = \Rightarrow 9=12k\Rightarrow k=\frac{12}{9} =\frac{4}{3}$$ so for $k=4/3$ the graph passes through $(3,3)$.
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