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Find the locus of a point whose distance...

Find the locus of a point whose distance from (a, 0) is equal to its distance from the y-axis.

Text Solution

Verified by Experts

The correct Answer is:
`y^2-2ax+a^2=0`
Let the point be (h,k). Therefore,
`(h-a)^2+(k-0)^2=h^2`
or `h^2+a^2-2ah+k^2=h^2`
Hence the locus is `y^2-2ax+a^2=0`.
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Knowledge Check

  • The locus of a point whose distance from (-2, 0) is (2)/(3) times its distance from the line x = (-9)/(2) is

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  • The equation of the locus of the point whose distance from y-axis is half the distance from origin is

    A
    `x^(2)+3y^(2)=0`
    B
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    D
    `3x^(2)-y^(2)=0`

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