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Q.

If $2 x^{2} - 5 x y + 2 y^{2} = 0$ represents two sides of a triangle whose centroid is (1, 1) then the equation of the third side is

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a

$x - y + 3 = 0$

b

$x + y - 3 = 0$

c

$x - y - 3 = 0$

d

$x + y + 3 = 0$

answer is A.

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Detailed Solution

$a = 2, 2 h = - 5, b = 2, (x_{1}, y_{1}) = (1, 1)$

Equation of third side is $S_{1} = \frac{3}{2} S_{11}$

$a x x_{1} + h (x y_{1} + x_{1} y) + b y y_{1}$

$= \frac{3}{2} (a x_{1}^{2} + 2 h x_{1} y_{1} + b y_{1}^{2})$

$\Rightarrow x + y - 3 = 0$

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If 2x2−5xy+2y2=0 represents two sides of a triangle whose centroid is (1, 1) then the equation of the third side is