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Write the equation of the circle passing...

Write the equation of the circle passing through (3,4) and touching y-axis at the origin.

Text Solution

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Give: the circle passes through origin and touches the Y-axis.

Hence, the centre lies on the X-axis. coordinates of centre are `(a, 0 )`.

Given: the circle passes through `(3,4)`

Hence,` sqrt{(a-3)^{2}+(0-4)^{2}}=a `

`Rightarrow a^{2}+9-6 a+16=a^{2} `

`Rightarrow-6 a+25=0`

`Rightarrow a=frac{25}{6}`

Hence, Required equation of circle is

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Knowledge Check

  • The equation of a circle passing through (3,-6) touching both the axes is

    A
    `x^(2)+y^(2) -6x -6y+9=0`
    B
    `x^(2)+y^(2)+6x-6y +9=0`
    C
    `x^(2)+y^(2)+30x -30y+225=0`
    D
    `x^(2)+y^(2)-30x-30y+225=0`

  • Equation of a circle which passes through (3,6) and touches the axes is

    A
    `x^(2)+y^(2)+6x+6y+3=0`
    B
    `x^(2)+y^(2)-6x-6y-9=0`
    C
    `x^(2)+y^(2)-6x-6y+9=0`
    D
    `"none of these"`

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