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

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$x - y + 3 = 0$

$x + y - 3 = 0$

$x + y - 1 = 0$

$x + y - 6 = 0$

answer is C.

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Detailed Solution

Given $2 x^{2} - 5 x y + 2 y^{2} = 0$ represent 2 equal sides and $(\frac{3}{2}, \frac{3}{2})$ lies on 3^rd line check option (3) verification.

$x + y - 3 = 0$

$= \frac{3}{2} + \frac{3}{2} - 3$

$= 6 - 6 = 0$

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