AP EAMCET2013MathematicsPair of Lines
aligned & If the & a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 aligned equation represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is
Options
- Ac(a+b)-a f^2-b g^2 a b-h^2
- Bc(a+b)+f^2+g^2 a b-h^2
- Cc(a+b)-f^2-g^2 a b-h^2
- Dc(a+b)-f^2-g^2 (a b-h^2 )^2
Correct answer
C. c(a+b)-f^2-g^2 a b-h^2
Step-by-step solution
We know that the point of intersection of the pair of straight line is ( f^2-b c h^2-a b , g^2-a c h^2-a b ) Required distance = [ ( f^2-b c h^2-a b -0 )^2+ ( g^2-a c h^2-a b -0 )^2 ]^2 aligned & = f^2-b c h^2-a b + g^2-a c h^2-a b & = f^2+g^2-c(a+b) h^2-a b & = c(a+b)-f^2-g^2 a b-h^2 aligned