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The equation of the circle having its ce...

The equation of the circle having its centre on the line `x+2y-3=0` and passing through the points of intersection of the circles `x^2+y^2-2x-4y+1=0a n dx^2+y^2-4x-2y+4=0` is `x^2+y^2-6x+7=0` `x^2+y^2-3y+4=0` c.`x^2+y^2-2x-2y+1=0` `x^2+y^2+2x-4y+4=0`

A

`x^(2)+y^(2)-6x +7=0`

B

`x^(2)+y^(2)-3y+4=0`

C

`x^(2)+y^(2)-2x-2y+1=0`

D

`x^(2)+y^(2)-2x-4y+4=0`

Text Solution

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A
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The equation of the circle having its centre on the line x+2y-3=0 and passing through the points of intersection of the circles x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)-4x-2y+4=0 is

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Knowledge Check

  • The equation of the circle having centre (0, 0) and passing through the point of intersection of the lines 4x + 3y = 2 and x + 2y = 3 is

    A
    `x^(2) + y^(2) = sqrt(5)`
    B
    `x^(2) + y^(2) = 5`
    C
    `x^(2) + y^(2) = 4`
    D
    `x^(2) + y^(2) = 2`

  • The circles x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)+4y-1 =0

    A
    touch internally
    B
    touch externally
    C
    have `3x+4y-1=0` as the common tangent at the point of contact.
    D
    have `3x+4y+1=0` as the common tangent at the point of contact.

  • The equation of the line passing through the intersection of the circles 3x^(2) +3y^(2) -2x +12y -9=0 and x^(2)+y^(2)+6x+2y-15=0 is

    A
    `8x-10y-7=0`
    B
    `10x-3y-27=0`
    C
    `4x+10y-5=0`
    D
    none

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