Q. The slope of tangents drawn form a point $(4,\ 10)$ to the parabola $y^{2} = 9x$ are
A) $\frac{1}{4},\frac{3}{4}$
B) $\frac{1}{4},\frac{9}{4}$
C) $\frac{1}{4},\frac{1}{3}$
D) None of these
Explanation
(b)
The equation of a tangent to the given parabola is
$y = mx + \frac{9}{4m}$
If it passes through (4,10), then
$10 = 4m + \frac{9}{4m}$
$\Rightarrow \ 16m^{2} - 40m + 9 = 0$
$\Rightarrow (4m - 1)(4m - 9) = 0\ \Rightarrow m = \frac{1}{4},\ \frac{9}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.