﻿ A focal chord of parabola y2 = 4x is inclined at an angle of  with the +ive direction of x-axis, then the slope of normal drawn at the ends of focal chord will satisfy the equation : Kaysons Education

# A Focal Chord Of Parabola y2 = 4x is Inclined At An Angle Of  with The +ive Direction Of X-axis, Then The Slope Of Normal Drawn At The Ends Of Focal Chord Will Satisfy The Equation

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## Question

### Solution

Correct option is

m2 + 2m – 1 = 0

Let A, B be the points (t12, 2t1) and (t22, 2t2), (a = 1) be two pints on the parabola y2 = 4x.

Since AB is a focal chord, t­1 t­2 = –1.

Also slope of chord y(t1 + t2) – 2x – 2at­1t2 = 0 is

Hence t1, t2 are the roots of

m2 – 2m – 1 = 0

Slopes of normal’s at A and B are – t1, – t2 which are roots of

(–m)2 – 2(–m) – 1 = 0

m2 + 2m – 1 = 0

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