Question

The slope of tangents drawn from a point $(4,10)$ to the parabola $y^2=9x$ are

• A. $\frac{1}{4},\frac{3}{4}$
• B. $\frac{9}{4},\frac{1}{4}$
• C. $\frac{1}{3},\frac{1}{4}$
• D. None of these

Answer 1

The correct option is B $\frac{9}{4},\frac{1}{4}$

We know that, the equation of tangent to the parabola $y^2=4ax$ is
$y=mx+\frac{a}{m}....\left(i\right)$
Here, given equation is $y^2=9x$
$\therefore a=\frac{9}{4}$
$\therefore$ Eq. (i) becomes
$y=mx+\frac{9}{4m}$
Since, it passes through $(4,10)$
$\therefore 10=4m+\frac{9}{4m}$
$\Rightarrow 16m^2-40m+9=0$
$\Rightarrow (4m-1)(4m-9)=0$
$\Rightarrow m=\frac{1}{4},\frac{9}{4}$.