Question

The line $x+y=6$ is a normal to the parabola $y^2=8x$ at the point

• A. $(18,-12)$
• B. $(4,2)$
• C. $(2,4)$
• D. $(8,8)$

Answer 1

The correct option is C $(2,4)$

Slope of the normal $x+y=6$ is $m_1=-1$

Then the slope of the Tangent at the same point is $m=\frac{-1}{m_1}=1$

Slope of the tangent for the given curve at point $(x_1,y_1)$ is given as

$2y_1.m=8\Rightarrow y_1=4\Rightarrow x_1=2$

point is $:(2,4)$