Question

Find the locus of the midpoints of chords of hyperbola `3x^(2)-2y^(2)+4x-6y=0` parallel to y = 2x.

Answer 1

Using `T = S_(1),` the equation of chord whose midpoint is (h, k) is
`3xh-2yk+2(x+h)-2y(y+k)=3h^(2)-2k^(2)+4h-6k`
`"or "x(3h+2)-y(2k+3)+…=0.`
Its slope is `(3h+2)/(2k+3)=2` as it is parallel to y = 2x.
`rArr" "3h-4k=4`
`rArr" "3x-4y=4,` which is required locus.