If the circle `x^2+y^2+2a_1x+c=0` lies completely inside the circle `x^2+y^2+2a_2x+c=0` then

If the circle x^2+y^2=1 is completely contained in the circle x^2+y^2+4x+3y+k=0 , then find the values of kdot

Statement 1 : The locus of the center of a variable circle touching two circle (x-1)^2+(y-2)^2=25 and (x-2)^2+(y-1)^2=16 is an ellipse. Statement 2 : If a circle S_2=0 lies completely inside the circle S_1=0 , then the locus of the center of a variable circle S=0 that touches both the circles is an ellipse.

If the circumference of the circle x^2 + y^2 + 8x + 8y - b = 0 is bisected by the circle x^2 + y^2 - 2x + 4y + a = 0 then a+b= (A) 50 (B) 56 (C) -56 (D) -34

If the circumference of the circle x^2+y^2+8x+8y-b=0 is bisected by the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is

The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle x^2+y^2-8x+6y+20=0 . Find the coordinats of the corresponding point of contact.

If the chord of contact of the tangents drawn from a point on the circle x^2+y^2=a^2 to the circle x^2+y^2=b^2 touches the circle x^2+y^2=c^2 , then prove that a ,b and c are in GP.

Consider the circle x^2 + y^2 + 8x + 10y - 8 = 0 (i) Find its radius of the circle x^2 + y^2 + 8x + 10y - 8 = 0 (ii) Find the equation of the circle with centre at C and passing through (1,2).

Consider a circle x^2+y^2+a x+b y+c=0 lying completely in the first quadrant. If m_1a n dm_2 are the maximum and minimum values of y/x for all ordered pairs (x ,y) on the circumference of the circle, then the value of (m_1+m_2) is

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0