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