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A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. If the tangent to the curve C cuts the corrdinate axes at A and B, then the locus of the middle point of AB is |
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Answer» `x^(2)=4y` The equation of TANGENT of P is `x*4t=(16(y+t^(2)))/(2)` `"or"4txx=8y+8t^(2)` `"or"tx=2y+2t^(2)` `A-=(2t,0), B-=(0,t^(2))` LTBRGT M(H,k) is the middle point of AB. `h=t,k=-(t^(2))/(2)or2k-h^(2)` Therefore, the locus of `M(h,k)` is `x^(2)+2y=0`. |
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