Question
Find the locus of the midpoints of the chords of the hyperbola which subtend a right angle at the origin.




None of these
diffcult
Solution
Let (h, k) be the midpoint of the chord of the hyperbola. Then its equation is
The equation of the lines joining the origin to the points of intersection of the hyperbola and the chord (i) is obtained by making homogeneous hyperbola with the help of (i)
The lines represented by (ii) will be at right angle if
Coefficient of x^{2} + Coefficient of y^{2} = 0
Hence, the locus of (h, k) is
.
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