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A: The equation of the circle (2,-3), (-...

A: The equation of the circle (2,-3), (-3,2) as ends of a diameter is `x^(2)+y^(2)+x+y-12=0`
R: The equation of the circle having the line segment joining `A(x_(1),y_(1)) and B(x_(2),y_(2))` as diameter `(x-x_(1)) (x-x_(2))+(y-y_(1)) (y-y_(2))=0`

A

Both A and R are true and R is the correct explanation of A

B

Both A and R are true and R is not the correct explanation of A

C

A is true but R is false

D

A is false but R is false

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If x - y + 1 = 0 meets the circle x^(2) + y^(2) + y - 1 = 0 at A and B , then the equation of the circle with AB as diameter is

    A
    `2(x^(2) + y^(2)) + 3x - y + 1 = 0 `
    B
    `2(x^(2) + y^(2)) + 3x -y + 2 = 0 `
    C
    `2(x^(2) + y^(2)) + 3x - y + 3 = 0 `
    D
    `x^(2) + y^(2) + 3x - y + 1 = 0 `

  • The equation of the circle described on the chord 3x+y+5=0 of the circle x^(2) +y^(2) =16 as diameter is

    A
    `x^(2) +y^(2) +3x +y-11=0`
    B
    ` x^(2) +y^(2) +3x +y+1=0`
    C
    ` x^(2) + y^(2) +3x +y-2 =0`
    D
    ` x^(2) +y^(2) +3x +y-22=0 `

  • If the circle x^2+y^2+2x+3y+1=0 cuts another circle x^2+y^2+4x+3y+2=0 in A and B , then the equation of the circle with AB as a diameter is

    A
    `2x^2+2y^2+2x+6y+1=0`
    B
    `x^2+y^2+x+3y+3=0`
    C
    `x^2+y^2+x+6y+1=0`
    D
    `2x^2+2y^2+x+3y+1=0`

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