Q. The equation $12x^{2} + 7xy + ay^{2} + 13x - y + 3 = 0$, represents a pair of perpendicular lines. Then, the value of ‘$a$’ is
A) $\frac{7}{2}$
B) $- 19$
C) $- 12$
D) $12$
Explanation
(c)
On comparing the given equation with standard equation, we get $a = 12$ and $b = a$. We also know, if pair of straight lines is perpendicular, then coefficient of $x^{2} +$ coefficient of $y^{2} = 0\ or\ a + b = 0$
$\therefore 12 + a = 0\ \Rightarrow a = - 12$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.