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Find the values of a for which three dis...

Find the values of `a` for which three distinct chords drawn from `(a ,0)` to the ellipse `x^2+2y^2=1` are bisected by the parabola `y^2=4xdot`

Text Solution

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Let the middle point of the chord be `(t^(2),2t)`.
It must lie inside the ellipse. Therefore,`t^(2)+8t^(2)-1lt0`
or `r^(2)x+4ty=8t^(2)`
Let this passes through `(alpha,0)`. Then , `alphat^(2)=t^(4)+8t^(2)`
or `t^(4)+(8-alpha)t^(2)=0`
i.e., `t^(2)=0 or t^(2)=alpha-8`
i.e., `alpha=t^(2)+8`
So, `alpha in (8,4+sqrt(17))`
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