Q. The conditions that $ax + by + c = 0$ is tangent to the parabola $y^{2} = 4ax$, is
A) $a^{2} = b^{2} = c^{2}$
B) $a = b$
C) $b^{2} = c$
D) $b^{2} = a$
Explanation
(c)
Since, the line $y = \frac{1}{b}x - \frac{c}{b}$ is tangent to the parabola $y^{2} = 4ax$, then
$- \frac{c}{b} = \frac{a}{- \frac{a}{b}} \Rightarrow \ c = b^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.