If the equation $2 x^{2} - 5 x y + 2 y^{2} = 0$ represents two sides of an isosceles triangle then the equation of the third side passing through the point (3,3) is

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$x + y = 3$

$x + y - 6 = 0$

$x - y = 3$

$2 x - y = 3$

answer is D.

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Detailed Solution

Third side is parallel to bisector $h (x^{2} - y^{2}) = (a - b) x y$

$\Rightarrow \frac{- 5}{2} (x^{2} - y^{2}) = (2 - 2) x y$

$\Rightarrow x^{2} - y^{2} = 0 \Rightarrow x - y = 0, x + y = 0$

required line is parallel to $x + y = 0$

$\Rightarrow (x - 3) + (y - 3) = 0$

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