If the normals at two points x 1 , y 1 and x 2 , y 2 of the parabola y 2 = 4 x meets again on the parabola, where x 1 + x 2 = 8 , then y 1 - y 2 is equal to

Question

If the normals at two points x 1 , y 1 and x 2 , y 2 of the parabola y 2 = 4 x meets again on the parabola, where x 1 + x 2 = 8 , then y 1 - y 2 is equal to, 2, 3, 4, 2

MARKS App · Accepted Answer

Let, x 1 , y 1 ≡ t 1 2 , 2 t 1 & x 2 , y 2 ≡ t 2 2 , 2 t 2 Now, x 1 + x 2 = 8 and both the normals again meets on the parabola, ∴ t 1 2 + t 2 2 = 8 & t 1 t 2 = 2 On solving, we get, t 1 - t 2 2 = 4 ⇒ t 1 - t 2 = 2 ⇒ y 1 - y 2 = 4

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