Question

The angle between the normals to the parabola $y^2=24x$ at points $(6,12)$ and $(6,-12)$ is :

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D ${90}^{\circ }$

$y^2=24x\Rightarrow (6t^2,12t)$
$A(6,12)\Rightarrow t=1$
$B(6,-12)\Rightarrow t=-1$
Slope of normal at a point is $-t$
$\therefore$ Slope of normal at $A$ is $-1$
$\therefore$ Slope of normal at $B$ is $1$
Clearly $m_1{m}_2=-1$
$\therefore$ Angle between normals is ${90}^{\circ }$