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If two sides of a triangle are given by $3 x^{2} - 5 x y + 2 y^{2} = 0$ and its orthocenter is (2, 1) then the equation of the third side of the triangle is

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$5 x - 10 y = 21$

$10 x + 5 y - 1 = 0$

$10 x + 5 y = 21$

$5 x - 10 y + 1 = 0$

answer is D.

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Detailed Solution

$3 x^{2} - 5 x y + 2 y^{2} = 0 & o (l, m) = (2, 1)$

$a = 3 | 2 h = - 5 | b = 2$

Eq. of 3^rd side is

$l x + m y = \frac{a m^{2} - 2 h l m + b l^{2}}{a + b}$

$\Rightarrow 10 x + 5 y = 21$

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