The Locus Of The Middle Point Of The Chords Of Hyperbola 3x2 – 2y2 + 4x – 6y = 0 Parallel To y = 2x is

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Question

The locus of the middle point of the chords of hyperbola 3x2 – 2y2 + 4x – 6y = 0 parallel to y = 2x is

Solution

Correct option is

3x – 4y = 4

 

Given  3x2 – 2y2 + 4x – 6y = 0                           …… (1)

             y = 2x                                                    …… (2)

let (x1y1) be mid-point of chord of (1)

⇒ equation is

     (3x+ 2)x + (2y1 – 3)y1 + (2x1 – 3y1) = 3x12  2y12 + 4x1 – 6y1

Now slope  locus is 3x – 4y = 4

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