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

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 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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