Question

Equation(s) of the tangents drawn from $(4,10)$ to the parabola $y^2=9x$ is/are

• A. $x-4y+36=0$
• B. $9x-4y+4=0$
• C. $x-2y+4=0$
• D. $x-y+1=0$

Answer 1

Answer: (A), (B)

$9x-4y+4=0$

Equation of tangent for $y^2=4ax$ is
$y=mx+\frac{a}{m}\cdots \left(1\right)$
We have $y^2=9x$
$4a=9\Rightarrow a=\frac{9}{4}$
Now, we get
$y=mx+\frac{9}{4m}\cdots \left(2\right)$
Above tangent passes through $(4,10)$,
$\Rightarrow 10=4m+\frac{9}{4m}\Rightarrow 16m^2-40m+9=0\Rightarrow (4m-9)(4m-1)=0\Rightarrow m=\frac{9}{4},\frac{1}{4}$

Put $m=\frac{9}{4}$ in equation $\left(2\right)$
$\Rightarrow 4y-9x-4=0\Rightarrow 9x-4y+4=0$

Put $m=\frac{1}{4}$ in equation $\left(2\right)$
$\Rightarrow x-4y+36=0$