Pole and Polar of a Circle

Q.

P is point lying outside a cicle. 3 lines are drawn from P to the cicle so that they intersect the circle at 6 points as shown in the figure.

$P_1,P_2,P_3$ are points formed by intersections of tangents at A and B, C and D and E and F respectively.

1. P₁, P₂, P₃ are always collinear

2. No relation possible for P₁, P₂, P₃

3. P₁, P₂, P₃ may be collinear

4. P₁, P₂, P₃ cannot be collinear

Q.

What is the polar of the point (2, 3) with respect to the circle $x^2+y^2-2x-4y-4=0$

1. x + y = 10

2. x + y = 12

3. x -y = 6

4. x - y = 10