Question

The slope of a tangent to the parabola $y^2=9x$ which passes through the point $(4,10)$ is

• A. $\frac{9}{4}$
• B. $\frac{1}{4}$
• C. $\frac{3}{4}$
• D. $\frac{1}{3}$

Answer 1

Answer: (A), (B)

$\frac{9}{4}$
$\frac{1}{4}$

Equation of tangent to a parabola is $y=mx+\frac{a}{m}$

$\therefore y=mx+\frac{9}{4m}$

It passes through $(4,10)$

$\Rightarrow 10=4m+\frac{9}{4m}$

$16m^2-40m+9=0$

$m=\frac{9}{4},\frac{1}{4}$