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:

Question

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:, 8 3, 10 3, 2 3, 16 3

MARKS App · Accepted Answer

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

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