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Question: If line x + 2y = 2 intersect parabola y<sup>2</sup> = 8x at points A & B then \(\frac{1}{SA}\)+ \(\f...

If line x + 2y = 2 intersect parabola y2 = 8x at points A & B then 1SA\frac{1}{SA}+ 1SB\frac{1}{SB} = {‘S’ is focus}

A

12\frac{1}{2}

B

1

C

2

D

4

Answer

12\frac{1}{2}

Explanation

Solution

Focus (2, 0)

Ž line is focal chord & SA, SB are length of segments of focal chord

1SA\frac{1}{SA}+ 1SB\frac{1}{SB} = SA+SBSA.SB\frac{SA + SB}{SA.SB} = 1a\frac{1}{a} = 12\frac{1}{2}