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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Hyperbola

JEE Main · Mathematics · Hyperbola

The locus of middle points of chords of hyperbola 3x^ 2 - 2y^ 2 +...

The locus of middle points of chords of hyperbola 3x2−2y2+4x−6y=03x^{2} - 2y^{2} + 4x - 6y = 0 parallel to y=2xy = 2x is

Options

  1. A3x−4y=43x - 4y = 4
  2. B3y−4x+4=03y - 4x + 4 = 0
  3. C4x−3y=34x - 3y = 3
  4. D3x−4y=23x - 4y = 2

Correct answer

A. 3x−4y=43x - 4y = 4

Step-by-step solution

Let (h,k)( h, k ) is mid point of chord.

Then, its equation is T=S1T = {S}_{1}

∴ 3hx - 2ky + 2\left(x + h\right) - 3\left(y + k\right) = 3h^{2} - 2k^{2} + 4h - 6k

x(3h+2)+y(−2k−3)=3h2−2k2+2h−3kx\left(3h + 2\right) + y\left(- 2k - 3\right) = 3h^{2} - 2k^{2} + 2h - 3k

Since, this line is parallel to y=2x3h+22k+3=2→3h−4k=4y = 2x\dfrac{3h + 2}{2k + 3} = 2\to 3h - 4k = 4

Thus, locus of point is 3x−4y=43x - 4y = 4
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