If y = m x + c is the normal at a point on the parabola y 2 = 8 x whose focal distance is 8 units, then c is equal to:

Step-by-step solution

Let the point on the parabola be P ( a t 2 , 2 a t ) where a = 2. Given distance of this point from focus be 8 units ⇒     a t 2 - a 2 + 4 a 2 t 2 = 64 ⇒             a t 2 + 1 = 8 ⇒           t 2 + 1 = 4 ⇒ t 2 = 3 ⇒         t =  ± 3 Since y = m x + c is normal to the parabola ⇒ c = 2 a t + a t 3 ⇒ c = 10 3