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Differential Calculus> show that the curves 4x =y^2 and 4xy=k cu...

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show that the curves 4x =y^2 and 4xy=k cut at right angles,if k^2=512

taniska , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello student,
Please find the answer to your question below

$y^2 = 4x$
Slope of tangent:
$2yy' = 4$
$y' = \frac{2}{y}$ ..............(1)
$4xy = k$
$xy' + y = 0$
$y' = \frac{-y}{x}$ ...................(2)
$(1)\times (2) = -1$
$\Rightarrow x = 2$
Put in the equation, we have
$y = \sqrt{8}$
$k = 8\sqrt{8}$
$k^2 = 512$

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