Question

If the centroid of the triangle formed by the lines $2y^2+5xy-3x^2=0$ and $x+y=k$ is $(\frac{1}{18},\frac{11}{18})$, then the value of $k$ is

• A. $-1$
• B. $0$
• C. $1$
• D. none of these

Answer 1

The correct option is C $1$

Given lines may written as $y+3x=0,2y-x=0$ and $x+y=k$
Solving these three we get the vertices of required triangle, which are
$(0,0),(\frac{2k}{3},\frac{k}{3})$ and $(-\frac{k}{2},\frac{3k}{2})$
Thus centroid of the triangle is $(\frac{k}{18},\frac{11k}{18})$
Comparing with the given value we get, $\Rightarrow k=1$