The centroid of the triangle formed by the pair of straight lines `12x^2- 20xy+7y^2=0` and the line `2x-3y + 4 = 0 `is

Options

A. `((-7)/(3),(7)/(3))`
B. `((-8)/(3),(8)/(3))`
C. `((8)/(3),(8)/(3))`
D. `((4)/(3),(4)/(3))`

Answer

C

Explanation

The separate equation of pair of straight lines of `12x^2-20xy+7y^2=0` are `6x-7y=0 and 2x-y=0`
Thus , equation of sides of triangle are `6x-7y=0`,
`2x-y=0 and 2x-3y+4=0`
On solving these equation , we get the vertices of triangles `A(0,0)B(1,2)and C(7,6)`
`therefore` Centroid of triangle is `((0+1+7)/(0),(0+2+6)/(3))=((8)/(3),(8)/(3))`