Question

Three normals are drawn to the parabola $y^2=4x$ from the point (c, 0). These normals are real and distinct when

• A. c$=0$
• B. c$=1$
• C. c$=2$
• D. c$=3$

Answer 1

Answer: (D)

c$=3$

Any normal of Parabola $y^2=4x)$ is given by,
$y=mx-2am-a{m}^3$ (Here $a=1)$
Given it passes through $(c,0)$
$\Rightarrow m(m^2+2-c)=0$
so for normal to be real and distinct $2-c<0\Rightarrow c>2$
Thus option 'D' is correct choice.