Length of Tangent and Power of a Point

Q. 1.The circle to which two tangents can be drawn from origin is 1) x2+ y-8x-4y-3 0 2 ) x2 + y2 + 4x + 2y + 2 = 0 3 ) x2 + y2-8x + 6y + 1 = 0 4) both (2) &(3)

Q. Find the angle between pair of tangents drawn from point (3, 2) to the circle x^2+y^2-6x+4y-2=0

Q.

The common chord of the circle $x^2+y^2+4x+1=0$ and $x^2+y^2+6x+2y+3=0$ is

1. 

2. 

3. 

4. 

Q. Find the angle between pair of tangents drawn from (1, 3) to circle x^2+y^2-2x+4y-11=0

Q. Find the angle between pair of tangents drawn from (0, 0) to the circle x^2+y^2-14x+2y+25=0

Q.

If the ratio of the lengths of tangents from a point to the circles $x^2+y^2+4x+3$ = 0, $x^2+y^2-6x+5$ = 0 Is 1:2 then the locus of P is a circle whose centre is

1. (-11/3 , 0 )

2. (-11 , 6 )

3. (-11/5 , 0 )

4. (-22/3 , 0 )

Q. 18. If two tangents are drawn from the point (-2, -1) to the parabola y2=4x if a is the angle between these tangents than tan a =

Q.

The line $lx+my+n=0$ will be a tangent to the circle $x^2+y^2=a^2$ iff

1. 

2. 

3. 

4. 

Q.

A tangent is drawn to a circle of radius r from an external point P .If length of tangent from a point to the circle is twice the minimum distance between circle and the point, what is the length of the tangent?

1. $\frac{3}{2r}$

2. 3 r

3. $\frac{2r}{3}$

4. $\frac{4r}{3}$

Q. Let tangents are drawn from $P(3,4)$ to the circle $x^2+y^2=a^2$ touches the circle at $A$ and $B$. If area of $△PAB=\frac{192}{25}$ sq. units, then $a=$

Q. If the tangent at the point $P$ on the circle $x^2+y^2+6x+6y=2$ meets the straight line $5x-2y+6=0$ at point $Q$ on the $y$-axis, then the length of $PQ$ is

1. $4$ units
2. $2\sqrt{5}$ units
3. $5$ units
4. $3\sqrt{5}$ units

Q. Tangents drawn from point P(4, 0)tothecircleX^2+Y^2=8 touches it at the point A in the first quadrant.Find the coordinates of another point B on the circle such that AB=4

Q. Find the angle between pair of tangents drawn from point (3, 2) to the circle x^2+y^2-6x+4y-2=0

Q.

The circle $C_1:x^2+y^2=3$ having centre at origin, O intersects the parabola $x^2=2y$ at the point P in the first quadrant. Let the tangent to the circle $C_1$ at P touches other two circles $C_2$ and $C_3$ at $R_2$ and $R_3$, respectively. Suppose $C_2$ and $C_3$ have equal radii $2\sqrt{3}$ and centres $Q_2$ and $Q_3$, respectively. If $Q_2$ and $Q_3$ lie on the Y-axis then

1. $Q_2{Q}_3=12$

2. $R_2{R}_3=4\sqrt{6}$

3. area of the $\Delta O{R}_2{R}_{3}is6\sqrt{2}$

4. area of the $\Delta P{Q}_2{Q}_{3}is4\sqrt{2}$