The condition of representing the coincident lines by the general quadratic equation `f(x,y)=0` , is

Options

A. `Delta =0,h^2=ab`
B. `Delta =0 and a+b=0`
C. `Delta =0,h^2=ab, g^2=ac,f^2=bc`
D. `h^2=ab,g^2=ac and f^2=bc`

Answer

C

Explanation

The necessary and sufficient condition that the lines represented by `f(x,y)=ax^2+2hxy+by^2+2gx+2fy+c=0` are coincident , if `Delta=|{:(a,h,g),(h,b,f),(g,f,c):}|=0` and `h^2=ab,g^2=ac,f^2=bc` .