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question mark

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

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

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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