Question

Let L be a normal to the parabola $y^2=4x$. If L passes through the point (9, 6), then L is given by

• A. $y-x+3=0$
• B. $y+3x-33=0$
• C. $y+x-15=0$
• D. $y-2x+12=0$

Answer 1

Answer: (A), (B), (D)

$y-2x+12=0$

Normal to $y^2=4x$, is
$y=mx-2m-m^3$ which passes through (9, 6).
$\Rightarrow 6=9m-2m-m^3$
$\Rightarrow m^3-7m+6=0$
$\Rightarrow m=1,2,-3$
$\therefore$ Equation of normals are,
$y-x+3=0,y+3x-33=0$ and $y-2x+12=0$