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Integration by Parts

lf the curves...

Question

lf the curves $2 x^{2} + 3 y^{2} = 1$ and $a x^{2} + 4 y^{2} = 1$ cut orthogonally, the value of a is

A

\frac{4}{5}

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B

\frac{12}{5}

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C

\frac{5}{12}

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D

8

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Solution

The correct option is D $\frac{12}{5}$
$m_{1} = y^{'} = \frac{- 2 x}{3 y}$ -----(1)
$m_{2} = y^{'} = \frac{- a x}{4 y}$
$m_{1} m_{2} = - 1$
$\frac{2 a x^{2}}{12 y^{2}} = - 1$
$(2 - a) x^{2} = y^{2}$
$2 a = 12 (a - 2)$
$a = \frac{12}{5}$

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