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If the normal to the parabola y^(2)=4ax ...

If the normal to the parabola `y^(2)=4ax` at point `t_(1)` cuts the parabola again at point `t_(2)`.Then the minimum value of `t_(2)^(2)` is

Text Solution

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A normal at point `t_(1)` cuts the parabola again at `t_(2)`. Then,
`t_(2)=-t_(1)-(2)/(t_(1))`
`or" "t_(1)^(2)+t_(1)t_(2)+2=0`
Since `t_(1)` is real, discriminant is greater than 0. Therefore,
`t_(2)^(2)-8ge0`
`or" "t_(2)^(2)ge8`
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