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TANGENTS AND NORMALS find the condition for the following set of curves to intersect orthogonally x^2/a^2 – y^2/b^2 = 1 and xy = c^2

TANGENTS AND NORMALS
 
find the condition for the following set of curves to intersect orthogonally
x^2/a^2 – y^2/b^2 = 1 and xy = c^2

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello student,
Please find the answer to your question below

Equation of curves:
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
xy = c^2
Two curves cut orthogonally, if tangents at point of contact are perpendicular
1st curve
\frac{2x}{a^2} - \frac{2yy'}{b^2}=0
y' = \frac{b^2x}{a^2y}…......(1)
2nd curve
y + xy' = 0
y' = \frac{-y}{x}.............(2)
(1)\times (2) = -1
\frac{b^2x}{a^2y}\times \frac{-y}{x} = -1
a^2 = b^2
a = b

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