COMEDK2018MathematicsStraight Lines
If the line p x+q y=0 coincides with one of the lines given by a x²+2 h x y+b y²=0 , then
Options
- Aa p²+2 h p q+b q²=0
- Ba q²+2 h p q+b p²=0
- Ca q²-2 h p q+b p²=0
- DNone of these
Correct answer
C. a q²-2 h p q+b p²=0
Step-by-step solution
The equation a x²+2 h x y+b y²=0 can be rewritten as a+ 2 h y x +b ( y x )²=0 Consider, p x+q y=0 p x=-q y y x = -p q Substituting in Eq. (i), we get aligned & a+2 h (- p q )+b ( -p q )²=0 a- 2 h p q +b p² q² =0 & a q²-2 h p q+b p²=0 aligned