Circle and Syst...

If P and Q are the points of intersection of the circles x² + y² + 3x + 7y + 2p - 5 = 0 and x² + y² + 2x + 2y - p² = 0, then there is a circle passing through P, Q and (1, 1) for

The number of common tangents to the circles x² + y² - y = 0 and x² + y² + y = 0 is

For two circles x² + y² = 16 and x² + y² - 2y = 0 there is/ are

The equation of the circle which cuts orthogonally the circle x² + y² - 6x + 4y - 3 = 0, passes through (3, 0) and touches the y - axis, is

If the point (3, - 4) lies on both the circles x² + y² - 2x + 8y + 13 = 0 and x² + y² - 4x + 6y + 11 = 0, Then the angle between the circles is

Consider a family of circles, which are passing through the point (-1,1) and are tangent to X-axis. If (h,k) are the coordinates of the centre of the circles, then the set of values of k is given by the interval

The value of k, so that x² + y² + kx + 4y + 2 = 0 and 2(x² + y²) - 4x - 3y + k = 0 cut orthogonally, is

The equations of the three circles are x² + y² - 6x - 6y + 4 = 0, x² + y² - 2x - 4y + 3 = 0 and x² + y² + 2kx + 2y + 1 = 0. If the radical centre of the above three circles exist, then which of the following cannot be the value of k?

The radical centre of the circles x² + y² - 16x + 60 = 0, x² + y² - 12x + 27 = 0 and x² + y² - 12y + 8 = 0 is

C₁is a circle of radius 2 touching the X-axis and the Y-axis. C₂ is another circle of radius > 2 and touching the axes as well as the circle C₁. Then, the radius of C₂ is