If a circle C, whose radius is 3, touches externally the circle,
$${x^2} + {y^2} + 2x - 4y - 4 = 0$$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

If the tangent at (1, 7) to the curve x² = y - 6

touches the circle x² + y² + 16x + 12y + c = 0, then the value of c is :

The tangent to the circle C₁ : x² + y² $$-$$ 2x $$-$$ 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C₂ whose center is (3, $$-$$2). The radius of C₂ is :

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $$y - 4x + 3 = 0,$$ then its radius is equal to :