Question

If y = mx+c is the normal at a point on the parabola y2=8x whose focal distance is 8 units, then |c| is equal to :

Answer 1

Please see the attachment

Answer 2

Solution :-

Given

parabola is y2 = 8x

on compaering this Parabola to

y^2 = 4ax,

we get a= 2

focal distance = distance of any point parabola from tha focus

here focus is S (2,0)

let any point on prabhola be P (X1 , Y1)

focal distance of Point P = SP

=>

$\sqrt{(x1 - 2) ^{2}} + (y1 - 0) ^{2} \\ \sqrt{x1^{2} - 4x1 + 4 + y1 ^{2} } \\ \sqrt{x1^{2} - 4x1 + 4 + 8x1 } \\ \sqrt{(x1 + 2)^{2} } = |x1 + 2|$

given that,

|x1 +2 | = 4

=> x1+2 = +_ 4

=> x1 = 2 , -6

=> but X ≠ -6

=> for X = 2

y1^2 = 8×2 = 16

y1 = +-4

so the point are (2,4) and (2,-4 )

=================

@GauravSaxena01