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A point P(x,y) moves in the xy - plane i...

A point P(x,y) moves in the xy - plane in such a way that its distance from the point (0,4) is equal to `(2)/(3)` rd of its distance from the x axis , find the equation to the locus of P.

Text Solution

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The correct Answer is:
`9x^(2)+5y^(2)-72y+144=0`
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A point moves in a plane such that its distance from the point (2,3) exceeds its distance from the y- axis by 2 . Find the equation to the locus of the point .

The distance of a point P from the striaght line x=-4 is equal to its distance from the point (3,0) . Find the equation to the locus of P.

Knowledge Check

  • A point moves in the xy -plan such that three times its distance from the y- axis exceeds two times its distance from the x- axis by 4. Then the equation to the moving points is -

    A
    `2x-3y=4`
    B
    `3x+2y=4`
    C
    `3x-2y=4`
    D
    `3x-2y+4=0`

  • A point moves in the xy - plane in such a manner that its distance from the origin is always 3 unit . State which of the following is the equation to the locus of the moving point ?

    A
    `x+y=3`
    B
    `x^(2)+y^(2)=3`
    C
    `x+y=9`
    D
    `x^(2)+y^(2)=9`

    • Similar Questions

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    A point moves in such a manner that 3 times its distance from the x-axis is greater than 4 times its distance from the y-axis by 7 , find the equation of its locus .

    A point moves in such a way that its ditance from the point (2,5) is equal to its distace from the line 2x + 4y = 3 . Find the equation of its path . What is the name of the curve ?

    A point moves in the xy - plane in such a way that its distances from the x-axes and the point (1,-2) are always equal . Find the eqution to its locus.

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

    Find the locus of a moving point whose distance from the point(1,-1,2) is always equal to the distance from x axis

    A point moves such that its distance from the y-axes is equal to its distance from the point (2,0). Find its locus and identify the nature of the conic .

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