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If the circle x^(2) + y^(2) -4x + 6y + a...

If the circle `x^(2) + y^(2) -4x + 6y + a =0` has radius 4, find a.

Text Solution

Verified by Experts

The correct Answer is:
`= -3`
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If the circle x^(2)+y^(2)-4x+6y+a = 0 has radius 4 then find a.

Find the value of a if 2x^(2)+ay^(2)-2x+2y-1=0 represents a circle and also find its radius. (ii) Find the values of a,b if ax^(2)+bxy+3y^(2)-5x+2y-3=0 represents a circle. Also find the radius and centre of the circle. (iii) If x^(2)+y^(2)+2gx+2fy=0 represents a circle with centre (-4,-3) then find g,f and the radius of the circle. (iv) If the circle x^(2)+y^(2)+ax+by-12=0 has the centre at (2,3) then find a ,b and the raidus of the circle. (v) If the circle x^(2)+y^(2)-5x+6y-a=0 has radius 4 , find a

Knowledge Check

  • The equation of the diameter of the circle x^(2) + y^(2) -4x-6y +3 = 0 that is perpendicular 2x + 5y-6 = 0 is

    A
    `5x - 2y= 4`
    B
    `5x +2y = 4`
    C
    `5x- 2y = -4`
    D
    `5x + 2y = -4`

  • The locus of the centre of the circle which cuts the circles x^(2) + y^(2) + 4x - 6y + 9 = 0 " and " x^(2) + y^(2) - 4x + 6y + 4 = 0 orthogonally is

    A
    ` 8x + 12y - 5= 0 `
    B
    `8x - 12y + 5 = 0 `
    C
    `4x - 6y + 5 = 0 `
    D
    none

  • The locus of the centre of the circle which cuts the circles x^(2) + y^(2) + 4x - 6y + 9 = 0 " and " x^(2) + y^(2) - 5x + 4y + 2 = 0 orthogonally is

    A
    `3x + 4y - 5 = 0 `
    B
    ` 9x - 10y + 7 = 0 `
    C
    `9x + 10y - 7 = 0 `
    D
    `9x - 10y + 11 = 0 `

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    The inverse of the point (1, 2) with respect to the circle x^(2) + y^(2) - 4x - 6y + 9 = 0 is

    If the circle x^(2) + y^(2) + 4x - 6y + c = 0 bisects the circumference of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 , then c is equal to

    If the circle x^(2) + y^(2) + 4x - 6y - c = 0 bissects the circumference of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 , then c =

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