AP EAMCET2001MathematicsPair of Lines
If one of the lines of pair of straight lines a x^2+2 h x y+b y^2=0 bisects the angle between the coordinate axes, then
Options
- Aa^2+b^2=h^2
- B(a+b)^2=4 h^2
- Ca^2+b^2=4 h^2
- D(a+b)^2=h^2
Correct answer
B. (a+b)^2=4 h^2
Step-by-step solution
The given pair of straight lines is array rlrl & a x^2+2 h x y+b y^2 & =0 & & m₁+m₂ & = -2 h b & and & m₁ m₂ & = a b array m₁= 45^ =1 Here, Then, the equation of the line is y=x . We have, array rlrl & & a x^2+2 h x^2+b x^2 & =0 & a+2 h+b & =0 & a+b & =-2 h & & a+b)^2 & =4 h^2 array