JEE MAIN - Mathematics (2021 - 26th August Evening Shift - No. 10)
The locus of the mid points of the chords of the hyperbola x2 $$-$$ y2 = 4, which touch the parabola y2 = 8x, is :
y3(x $$-$$ 2) = x2
x3(x $$-$$ 2) = y2
y2(x $$-$$ 2) = x3
x2(x $$-$$ 2) = y3
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
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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