The point of intersection of the lines represented by the equation `2x^2+3y^2+7xy+8x+14y+8=0` is

Options

A. `(0,2)`
B. `(1,2)`
C. `(-2,0)`
D. `(-2,1)`

Answer

C

Explanation

Let `f(x,y)=2x^2+3y^2+7xy+8x+14y+8`
The point of intersection of the pain of lines given by
`((bg-hf)/(h^2-ab),(af-gh)/(h^2-ab))=[(3xx4-(7)/(2)xx7)/(((7)/(2))^2-2xx3),(2xx7-4xx(7)/(2))/(((7)/(2))^2-2xx3)]=(((25)/(2))/((25)/(4)),(0)/((25)/(4)))=(-2,0)`
`therefore` Required point of intersection is `(-2,0)`.