If the circles `x^2+y^2-9=0` and `x^2+y^2+2alpha x+2y+1=0` touch each other, then `alpha` is (a)`-4/3` (b) 0 (c) 1 (d) `4/3`

If the circles x^2 + y^2 + 2ax + b = 0 and x^2+ y^2+ 2cx + b = 0 touch each other (a!=c)

If the circle x^2 + y^2 + ( 3 + sin beta) x + 2 cos alpha y = 0 and x^2 + y^2 + 2 cos alpha x + 2 c y = 0 touch each other, then the maximum value of c is

The two circles x^2+y^2=ax and x^2+y^2=c^2(c > 0) touch each other if (1) a=2c (2) |a|=2c (3) 2|a|=c (4) |a|=c

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

The equation of the line inclined at an angle of pi/4 to the x-axis ,such that the two circles x^2+y^2=4 and x^2+y^2 -10 x-14 y+65=0 intercept equal length on it, is (A) 2x-2y-3=0 (B) 2x-2y+3=0 (C) x-y+6=0 (D) x-y-6=0

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot

If one end of a diameter of a circle 2x^2 + 2y^2 - 4x - 8y + 2 = 0 is (3,2), then the other end is

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+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 circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0