First slide

Pair of straight lines

Question

Equation, $2 x^{2} - 5 xy + 2 y^{2} = 0$ represents two sides of a triangle whose centroid is (2,3) then area of triangle is

Easy

A

2
B

6
C

18
D

0

Solution

Split the given equation $2 x^{2} - 5 xy + 2 y^{2} = 0$ as $(2 x - y) = 0$ and $(x - 2 y) = 0$
General points on both lines are $(l, 2 l), (2 m, m)$
Hence, the vertices of the triangle are $(0, 0), (l, 2 l), (2 m, m)$ is $(\frac{l + 2 m}{3}, \frac{2 l + m}{3}) = (2, 3)$
Equate corresponding co - ordinates and then solve for L , M
We get $l = 4, m = 1$
The vertices of triangle are (0, 0), (4, 8), (2, 1)
The area of the triangle formed by the above vertices is $\frac{1}{2} | (4 - 16) | = 6 square units$

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