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IF three distinct normals to the parabola `y^(2)-2y=4x-9` meet at point (h,k), then prove that `hgt4`. |
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Answer» Given parabola is `(y-1)^(2)=4(x-2)`. Equation of normal to parabola having slope m is `y-1=m(x-2)-2m-m^(3)` It passes through (h,k) `:." "k-1=m(h-2)-2m-m^(3)` `or" "m^(3)+(4-h)m+k-1=0` This equation has three distinct real roots. `:." "3m^(2)+(4-h)=0` has two distinct real roots. `:." "4-hlt0orhgt4` |
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