If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point ($$-$$30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5 $$ on the x-axis. Then the radius of the circle C is equal to :

Two tangents are drawn from the point P($$-$$1, 1) to the circle x² + y² $$-$$ 2x $$-$$ 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :