Question

The equation of normal to parabola y ^ 2 = 8x , which is parallel to line x - 2y + 8 = 0 is .​

Answer 1

Step-by-step explanation:

refer to the attachement

mark as brainliest

Answer 2

Given,

Equation of parabola = $y^{2}=8x$,

Equation of line parallel to parabola's normal = x-2y+8=0,

To find,

Equation of normal

Solution,

The equation of a general parabola is,

$Y^{2}=4ax$

We have, $y^{2}=8x$,

Therefore, on comparing we get a=2,

Also, the Slope of the line parallel to the parabola's normal x-2y+8=0 is

$m=-\frac{coefficient of y}{coefficient of x}$,

$m=-\frac{(-2)}{1}$,

m=2,

since, the line is parallel to the normal of the parabola so,

slope of normal = slope of line = 2,

Normal equation:

⇒ $y = mx-2am-am^{3}$

⇒ $y=(2)x-2(2)(2)-(2)(2)^3$,

⇒ y=2x-8-16,

⇒ y=2x-24,

⇒ 2x-y-24=0.