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  4. The locus of the middle points of chords of the parabola y2=8x drawn through the vertex is a parabola whose

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Q. The locus of the middle points of chords of the parabola $ {{y}^{2}}=8x $ drawn through the vertex is a parabola whose

Jharkhand CECEJharkhand CECE 2012

Solution:

If the middle point of a chord is $ (\alpha ,\,\,\beta ), $ then $ \alpha =\frac{2{{t}^{2}}+0}{2},\,\,\beta =\frac{4t+0}{2} $
On eliminating $ t $ , we get $ \alpha ={{\left( \frac{\beta }{2} \right)}^{2}} $
$ \therefore $ Locus is $ x=\frac{{{y}^{2}}}{4} $
$ \Rightarrow $ $ {{y}^{2}}=4x $
This is the equation of parabola with latusrectum $ 4 $