Pole and Polar of a Circle

Q.

A tangent is drawn to the parabola $y^2=6x$ which is perpendicular to the line $2x+y=1$. Which of the following points does NOT lie on it?

1. $(0,3)$

2. $(-6,0)$

3. $(4,5)$

4. (5, 4)

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

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

Q. If $ax+by+c=0$ is the polar of $(1,1)$ for the circle $x^2+y^2-2x+2y+1=0$ and $H.C.F.$ of $b,c$ is equal to $1$, then the value of $a^2+b^2+c^2$ is

1. $0$
2. $3$
3. $5$
4. $15$

Q.

Polar of a point can exist only when the point is outside the circle.

1. True

2. False

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. 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.

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. If $ax+by+c=0$ is the polar of $(1,1)$ for the circle $x^2+y^2-2x+2y+1=0$ and $H.C.F.$ of $b,c$ is equal to $1$, then the value of $a^2+b^2+c^2$ is

1. $3$
2. $5$
3. $0$
4. $15$

Q.

What is the equation of polar of the point (1, 2) with respect to the circle $x^2+y^2+8x+2y+1=0$

1. $5x-3y-7=0$

2. $5x+3y+7=0$

3. $3x+5y+1=0$

4. $3x-5y-1=0$

Q.

Polar of a point can exist only when the point is outside the circle.

1. True

2. False

Q.

P is a point situated inside a circle. Line 'l' is the polar of point P. Then chord of contact of any point from the line 'l' passes through point p.

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. P₁, P₂, P₃ cannot be collinear

2. No relation possible for P₁, P₂, P₃

3. P₁, P₂, P₃ may be collinear

4. P₁, P₂, P₃ are always collinear

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.

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

Q.

What is the equation of polar of the point (1, 2) with respect to the circle $x^2+y^2+8x+2y+1=0$

1. 

2. 

3. 

4. 

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 = 12

2. x -y = 6

3. x - y = 10

4. x + y = 10

Q.

P is a point situated inside a circle. Line 'l' is the polar of point P. Then chord of contact of any point from the line 'l' passes through point p.

1. True

2. False

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. $x-y=10$

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. The number of solution(s) of the equation $3\tan (x-\frac{\pi }{12})=\tan (x+\frac{\pi }{12})$ in $A=\{x\in R:x^2-6x\le 0\}$ is

Q.

The number of values of $x\in (0,\pi )$ satisfying the equation $\sin x+\sqrt{3}\cos x=\sqrt{2}$ is

1. $3$
2. $1$
3. $2$
4. $0$

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. $x-y=10$