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 :

A line drawn through the point P(4, 7) cuts the circle x² + y² = 9 at the points A and B. Then PA⋅PB is equal to :