First slide

Pair of straight lines

Question

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

Moderate

A

$x + y - 3 = 0$
B

$x - y - 3 = 0$
C

$x + y + 3 = 0$
D

$x - y + 3 = 0$

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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