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A variable circle passes through the point `A(a ,b)` and touches the x-axis. Show that the locus of the other end of the diameter through `A` is `(x-a)^2=4b ydot`

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A variable circle passes through the point P (1, 2) and touches the x-axis. Show that the locus of the other end of the diameter through P is (x-1)^2 = 8y .

A variable circle passes through the fixed A (p, q) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-p)^2 = 4qy .

Knowledge Check

  • A variable circle passes through a fixed point (p, q) and touches the x-axis. The locus of the other end of the diameter through A is :

    A
    `(x-p)^(2)=4qy`
    B
    `(x-q)^(2)=4py`
    C
    `(y-p)^(2)=4qx`
    D
    `(y-q)^(2)=4px`

  • A variable circle passes through a fixed point A(a,b) and touches the axis of x. Locus of the other end of the diameter through A is

    A
    circle
    B
    parabola
    C
    ellipse
    D
    none of these

  • A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is:

    A
    `(y-q)^(2) = 4px`
    B
    `(x-q)^(2) = 4py`
    C
    `(y-p)^(2) = 4qx`
    D
    `(x-p)^(2) = 4qy`

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    A variable circle passes through the fixed point (2,0) and touches y-axis then the locus of its centre is

    A circle passes through A(1,1) and touches x - axis then the locus of the other end of the diameter through 'A' is

    The circle passing through the point (-1,0) and touching the y -axis at (0,2) also passes through the point:

    A variable circle passes through the fixed point (2, 0) and touches y-axis Then, the locus of its centre, is

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