If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 u…

Question

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

Accepted Answer

c = - 29m - 9m3

a = 2

Given (at2 - a)2 + 4a2t2 = 64

$$ \Rightarrow $$   (a(t2 + 1)) = 8

$$ \Rightarrow $$   t2 + 1 = 4 $$ \Rightarrow $$ t2 = 3

$$ \Rightarrow $$   t = $$\sqrt 3 $$

$$ \therefore $$   c = 2at(2 + t2)

= $$2\sqrt 3 \left( 5 \right)$$

$$\left| c \right|$$ = 10$$\sqrt 3 $$

Solutions · 1