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Find the coordinates of the middle point of the chord of the parabola y^2=16x,the equation of which is 2x-3y+8=0.
Sol:parabola is y^2=16xand str line 2x/3+8/3=yNow, abscica of two points of intersection are given by roots of 16x=4x^2/9+64/9+32x/9 or 0=4x^2/9-112x/9+64/9Absica of midpoint of chord is in this eq is =sum of roots /2=-b/2a=14similarly do this for ordinate hope you can proceed and find it to be 12so required answer is (14,12)
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