Question

Find the equations of the tangents of the parabola $y^2=12x$, which passes through the point $(2,5).$

• A. $3x-2y+4=0$
• B. $x-y+3=0$
• C. $x-y-3=0$
• D. $3x-2y-4=0$

Answer 1

Answer: (A), (B)

The correct options are
A $3x-2y+4=0$
B $x-y+3=0$

Given parabola is, $y^2=12x$
Here $a=3$
Thus equation of tangent to this parabola is given by,
$y=mx+\frac{a}{m}=mx+\frac{3}{m}$
Also this line passes through $(2,5)$
$\Rightarrow 5=2m+\frac{3}{m}\Rightarrow 2m^2-5m+3=0\Rightarrow m=1,\frac{3}{2}$
Thus equation of tangent to the given parabola passes through $(2,5)$ are,
$x-y+3=0$ and $3x-2y+4=0$