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Joint Entrance Examination
Mathematics
Hyperbola
Question 96
Question 96 of 106
Medium
MCQ
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
D
x2(x \[-\] 2) = y3
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Official 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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