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If the chord of contact of tangents from a point `P` to the parabola `y^2=4a x` touches the parabola `x^2=4b y ,` then the locus of `Pdot` is a) a cicle b) a parabola c) a straight line d) none of these

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Chord of contact of parabola `y^(2)=4ax` w.r.t. point `P(x_(1),y_(1))` is `yy_(1)=2a(x+x_(1))`.
Solving this line with parabola `x^(2)=4by`, we get
`x^(2)=4bxx(2a)/(y_(1))(x+x_(1))`
`ory_(1)x^(2)=8bx-8abx_(1)=0`
Since the line touches the parabola, this equation will have equal roots.
`:.` Discriminant, D = 0
`rArr" "64a^(2)b^(2)+32abx_(1)y_(1)=0`
`rArr" "x_(1)y_(1)=-2ab`
`rArr" "xy=-2ab`, which is the required locus.
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Knowledge Check

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