Equation,2x2-5xy+2y2=0  represents two sides of a triangle whose centroid is (2,3)  then area of triangle is

Split the given equation 2x2-5xy+2y2=0 as 2x-y=0  and  x-2y=0General points on both lines are  l,2l,2m,mHence, the vertices of the triangle are 0,0,l,2l,2m,m is  l+2m3,2l+m3=2,3Equate corresponding co - ordinates and then solve for   L , M We get  l=4,m=1The vertices of triangle are (0, 0), (4, 8), (2, 1)The area of the triangle formed by the above vertices is 12|(4−16)|=6 square units