From a point $A (1, 1)$ straight lines $A L$ and $A M$ are drawn at right angles to the pair of straight lines $3 x^{2} + 7 x y - 2 y^{2} = 0$ . Find the equation of pair straight lines $A L$ and $A M$ .

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Solution

Lines through origin perpendicular to give lines
$3 x^{2} + 7 x y - 2 y^{2} = 0$ is
$- 2 x^{2} - 7 x y + 3 y^{2} = 0$
or $2 x^{2} + 7 x y - 3 y^{2} = 0$ .
Hence lines through $A (1, 1)$ perpendicular to given lines
are
$2 (x - 1)^{2} + 7 (x - 1) (y - 1) - 3 (y - 1)^{2} = 0$
or $2 x^{2} + 7 x y - 3 y^{2} - 11 x - y + 6 = 0$ .
Above gives the equation of lines $A L$ and $A M$ .

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