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Find the locus of midpoints of the chords of the parabola {\frac  {x^{2}}{9}}-{\frac  {y^{2}}{4}}=1\, which are parallel to 3x+8y-4=0\,

Let P(x_{1},y_{1})\, be the midpoint of a chord of 4x^{2}-9y^{2}=36\,

Therefore,equation to the chord is 4xx_{1}-9yy_{1}=4x_{1}^{{2}}-9y_{1}^{{2}}\,

This is parallel to the line 3x+8y-4=0\,

Equating the slopes of the both

{\frac  {4x_{1}}{9y_{1}}}={\frac  {-3}{8}}\,

Therefore the locus of P is the line 32x+27y=0\,

Main Page:Geometry:Hyperbola