Question

A normal is drawn at a point $(x_1,y_1)$ of the parabola $y^2=16x$ and this normal makes equal angle with both $x$ and $y$ axes. Then point $(x_1,y_1)$ is

• A. $(4,-4)$
• B. $(2,-8)$
• C. $(4,-8)$
• D. $(1,-4)$

Answer 1

The correct option is C $(4,-8)$

$y^2=16x\Rightarrow 2y{y}^{\prime }=16\Rightarrow y^{\prime }=\frac{8}{y_1}$
Slope of the normal
$m_n=1\Rightarrow -\frac{y_1}{8}=1\Rightarrow y_1=-8$
$x_1=\frac{64}{16}=4$