Pole and Polar of a Circle

Q. The pole of $3x+4y-45=0$ with respect to the circle $x^2+y^2-6x-8y+5=0$ is

1. $(6,8)$
2. $(8,6)$
3. $(4,3)$
4. $(3,4)$

Q.

The polars drawn from (-1, 2) to the circle s$S_1\equiv x^2+y^2+6y+7=0$ and $S_2\equiv x^2+y^2+6x+1=0$, are

1. Equal

2. Perpendicular

3. Parallel

4. Intersect at a point

Q. Show that the locus of the middle points of the chords of a parabola passing through the vertex is a parabola.

Q.

True or False

Statement: Polar of the point $P(x_1,y_1)$ with respect to the circle $x^2+y^2=a^2$ is $x{x}_1+y{y}_1=a^2$ (P is inside the circle)

1. True

2. False

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. $P_1,P_2,P_3$ are always collinear

2. $P_1,P_2,P_3$ may be collinear

3. $P_1,P2,P_3$ cannot be collinear

4. No relation possible for $P_1,P_2,P_3$

Q. If $(1,-2)$ is a pole of the circle $x^2+y^2-10x-10y+25=0$, then the equation of the diameter which bisects the polar is

1. $2x+y-15=0$
2. $4x-7y+15=0$
3. $x-2y+5=0$
4. $7x-4y-15=0$

Q.

The point of intersection of the tangents of the circle $x^2+y^2=10$, drawn at end points of the chord x + y = 2 is

1. (5, 5)

2. (-5, -4)

3. (-4, -5)

4. None of these