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Normals are drawn to the parabola y^(2)=4x from any point on the line y=2, then vertices of the triangle formed by corresponding tangents lie on a fixed rectangular hyperbola xy=-c^(2) then c^(2) is ________

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SOLUTION :EQUATION of normal at `(t^(2),2t)` is `y=-xt+2t+t^(3)`
LET any POINT on `y=2` is `(h,2)`
If normal passes through `(h,2)`
`2+ht-2t-t^(3)=0`
`t^(3)-t(h-2)-2=0`
`t_(1),t_(2)` and `t_(3)` are points of this equation vertices lies on `xy=-2`


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