Question

The line y = 2x + k is a normal to the parabola $y^2=4x$ then k =

• A. 12
• B. -12
• C. 10
• D. -10

Answer 1

The correct option is B -12

$y=2x+k\Rightarrow 2x–y+k=0.Herel=2,m=–1,n=kanda=1$
$y=2x+kisanormalto{y}^2=4x\Rightarrow a{l}^2+2al{m}^2+m^{2}n=0$
$\Rightarrow 1(2{)}^3+2(1\left)\right(2\left)\right(-1{)}^2+k=0\Rightarrow k+12=0\Rightarrow k=-12$