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If the straight lines x-4y + 7=0 and 3x ...

If the straight lines `x-4y + 7=0` and `3x - 12y + 11 =0`
are tangents to a circle. Then, the radius of the circle is

A

`(10)/( 3 sqrt17)`

B

`(5)/( 3 sqrt7)`

C

`(15)/( sqrt17)`

D

`(5)/( 3 sqrt17)`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • The two diameters of a circle are segments of the straight lines x-y =5 and 2x+y =4 .If the radius of the circle is 5 then the equation of the circle is

    A
    `x^(2)+y^(2) -6x+4y =12 `
    B
    `x^(2) +y^(2) -3x+2y=12 `
    C
    `x^(2)+y^(2) -6x+2y=12 `
    D
    `x^(2)+y^(2) -8x +6y -18 =0`

  • If (3,-2) is the centre of a circle and 4x+3y +19 =0 is a tangent to the circle , then the equation of the circle is

    A
    `x^(2)+y^(2)-6x+4y+25=0`
    B
    `x^(2)+y^(2)-6x+4y+12=0`
    C
    `x^(2)+y^(2)-6x+4y-12=0`
    D
    `x^(2)+y^(2)-6x+4y+13=0`

  • The lines 2x -3y =5 and 3x-4y =7 are diameter of a circle having area as 154 sq. unit. Then , the equations of the circle is :

    A
    ` x^(2)+ y^(2) +2x - 2y = 62`
    B
    ` x ^(2) + y^(2)+ 2x- 2y= 47`
    C
    ` x^(2) +y^(2)-2x +2y =47`
    D
    ` x^(2)+ y^(2) - 2x + 2y =62`

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