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Find the locus of the midpoint of chords...

Find the locus of the midpoint of chords of the parabola `y^2=4a x` that pass through the point `(3a ,a)dot`

Text Solution

Verified by Experts

The correct Answer is:
`y^(2)-2ax-ay+6a^(2)=0`
Let the midpoint of the parabola be P(h,k).
So, equation of chord is
`ky-2a(x+h)=k^(2)-4ah`
This chord passes through the point (3a,a).
`:." "ak-2a(3a+h)=k^(2)-4ah`
So, locus of point P is `y^(2)-2ax-ay+6a^(2)=0`.
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