Length of Chord of Contact

Q.

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Q. The equation of the chord joining two points (x1, y1) and (x2, y2) on the rectangular hyperbola xy=c² is

Q. 29. Number of distinct chords of the circle 2x(x-2)+y(2y-1)=0 Passing through the point (2, 1/2) and are bisected by x-axis

Q. 5. Length of the common chord of the circle x2+y2+2x+3y+1=0andx2+y2+4x+3y+4=0

Q.

The number of common tangents(s) to the circles $x^2+y^2+2x+8y-23=0and{x}^2+y^2-4x-10y+19=0$ is

1. 4

2. 1

3. 2

4. 3

Q. Two circles $C_1$ and $C_2$ both passes through the points $A(1,2)$ and $E(2,1)$ and touch the line $4x-2y=9$ at $B$ and $D$ respectively. The possible cordinates of a point $C$ such that the quadrilateral $ABCD$ is a parallelogram is $(a,b)$ then the value of $|ab|$ is

Q. Tangents $PA$ and $PB$ are drawn to $x^2+y^2=4$ from the point $P(3,0).$ Then the area (in sq. units) of $△PAB$ is

1. $\frac{5}{9}\sqrt{5}$
2. $\frac{1}{3}\sqrt{5}$
3. $\frac{10}{9}\sqrt{5}$
4. $\frac{20}{3}\sqrt{5}$

Q.

Tangents are drawn from (4, 4) to the circle $x^2+y^2-2x-2y-7=0$ to meet the circle at A and B. The length of the chord AB is

1. $2\sqrt{3}$

2. $3\sqrt{2}$

3. $2\sqrt{6}$

4. $6\sqrt{2}$

Q.

Points P, Q and the centre of the circle O lies on a straight line. P, Q are both outside the circle. When chords of contact of P and Q are drawn to the circle they are found to coincide. Whats the distance between P and Q?

1. 

2. 2R or 0

3. 2R

4. At an unknown value between 2R and 4R

Q.

If the cicles $(x-1{)}^2+(y-3{)}^2=r^{2}and{x}^2+y^2-8x+2y+8=0$ intersect in two distinct points, then

1. r = 2

2. 2 < r < 8

3. r < 2

4. r > 2

Q. The equation of the chord joining two points (x_1, y_1) and (x_2, y_2) on the rectangular hyperbola xy=c^2 is

Q.

RS is the chord of contact of the point P on a circle center at O. if $m_1=slopeof\overline{RS}and{m}_2=slopeof\overline{OP}$

1. $m_1+m_2=0$

2. $\frac{m_1}{m_2}=+1$

3. $m_1-m_2=1$

4. $m_1.m_2=-1$

Q.

RS is the chord of contact of the point P on a circle center at O. if $m_1=slopeof\overline{RS}and{m}_2=slopeof\overline{OP}$

1. 

2. 

3. 

4. 

Q. The length of common chord of two intersecting circles is $30$cm. If the diameters of these two circles be $50$ cm and $34$ cm, then the distance between their centres is

Q.

Points P, Q and the centre of the circle O lies on a straight line. P, Q are both outside the circle. When chords of contact of P and Q are drawn to the circle they are found to coincide. Whats the distance between P and Q?

1. 2R or 0

2. 2R

3. At an unknown value between 2R and 4R

4. $\infty or0$