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The locus of the mid points of the chords of the hyperbola x2 $$-$$ y2 = 4, which touch the parabola y2 = 8x, is :

JEE · Math · previous-year question

  1. A.y3(x $$-$$ 2) = x2
  2. B.x3(x $$-$$ 2) = y2
  3. C.y2(x $$-$$ 2) = x3correct
  4. D.x2(x $$-$$ 2) = y3

Answer

C. y2(x $$-$$ 2) = x3

Explanation

T = S1 xh $$-$$ yk = h2 $$-$$ k2 $$y = {{xh} \over k} - {{({h^2} - {k^2})} \over k}$$ this touches y2 = 8x then $$c = {a \over m}$$ $$\left( {{{{k^2} - {h^2}} \over k}} \right) = {{2k} \over h}$$ 2y2 = x(y2 $$-$$ x2) y2(x $$-$$ 2) = x3

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