Question

if the line y=3x+c touches the parabola y^2=12x at point P, then the equation of tangent at Q where P,Q are ends of focal chord

Answer 1

Step-by-step explanation:

We have,

$\large \tt{ \bold{ Parabola \colon}}\:y^2=12x$

$\large \tt{ \bold{ Line \colon}}\:y=3x+c$

Now, the line will touch the parabola iff

$c = \pm \: a \sqrt{ {m}^{2} + 1 }$

Here, the equation of parabola may be written in the form of $y^2=4ax$, where, a=3,

so,

$c = \pm3 \sqrt{(3)^{2} + 1}$

$\implies \: c = \pm3 \sqrt{9 + 1}$

$\implies \: c = \pm3 \sqrt{ 10}$

So, equation of tangent at Q will be

$y = 3x + 3 \sqrt{10}$

OR

$y = 3x - 3 \sqrt{10}$