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A tangent to the parabola y^2=4ax meets ...

A tangent to the parabola `y^2=4ax` meets axes at A and B.Then the locus of mid-point of line AB is

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at`(x_1,y_1)`
`y^2=4ax`
diff. with respect to x
`yy'=2a(x+x_1)`
`2aty=2a(x+at^2)`
`ty=x+at^2`
`h=(0+(-at^2))/2`
`h=(-at^2)/2`
...
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