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Grade 12Differential Calculus

TANGENTS & NORMALS

show that the curves 2x=y^2 and 2xy=k cut at right angles if k^2=8

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$y^2 = 2x$
Slope of tangent:
$2yy' = 2$
$y' = \frac{1}{y}$ …..............(1)
$2xy = k$
Slope of tangent:
$xy' + y = 0$
$y' = \frac{-y}{x}$ ...............(2)
$\frac{1}{x} = 1$
$x = 1$
Put in the equation of curves:
$y = \sqrt{2}$
$k = 2y$
$k = 2\sqrt{2}$
$k^{2} = 8$

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