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

"T = S 1 xh $-$ yk = h 2 $-$ k 2 $y = {{xh} \\over k} - {{({h^2} - {k^2})} \\over k}$ this touches y 2 = 8x then $c = {a \\over m}$ $\\left( {{{{k^2} - {h^2}} \\over k}} \\right) = {{2k} \\over h}$ 2y 2 = x(y 2 $-$ x 2 ) y 2 (x $-$ 2) = x 3 "

Medium MCQ +4 / -1 PYQ · JEE Mains 2021

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

A y3(x $-$ 2) = x2
B x3(x $-$ 2) = y2
C y2(x $-$ 2) = x3 Correct answer
D x2(x $-$ 2) = y3

Solution

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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Subject: Mathematics · Chapter: Conic Sections · Topic: Parabola

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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 :

Solution

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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 :