Chord of Contact

Q. Let $x-2y+7=0$ be a chord of the circle $x^2+y^2-2x-10y+1=0$. If the midpoint of the chord is $P(\alpha ,\beta )$, then the value of $5|\alpha -\beta |$ is

Q. The locus of the point, whose chord of contact w.r.t the circle $x^2+y^2=a^2$ makes an angle $2\alpha$ at the centre of the circle is

1. 
2. 
3. 
4. 

Q.

The circle $x^2+y^2=4x+8y+5$ interesects the line 3x - 4y = m at two distinct points if
(2010)

1. -35 < m < 15

2. 15 < m < 65

3. 35 < m < 85

4. -85 < m < -35

Q.

2 tangents $P{T}_1$ and $P{T}_2$ are drawn as shown in the figure and PQ passes through the centre O of the circle. Which segment(s) is/are the chord of contact of P.

1. RQ

2. 

3. 

4. None of these

Q.

What is the range of lengths of chord of contact of a circle with radius R.

1. (0, R)

2. (O, 2R)

3. (R, 2R)

4. (O, )

Q.

What is the slope of the chord of contact of the point (6, -4) to the circle $x^2+y^2-2x-2y+1=0$

1. 0

2. -1

3. 1

4. 

Q.

In the circle given below which point(s) has/have a chord of contact.

1. Neither P and Q

2. P only

3. Both P and Q

4. Q Only

Q. The chords of contact of the pair of tangents drawn from each point on the line
$2x+y=4$ to the circle $x^2+y^2=1$ pass through the point ___.

1. $(\frac{1}{4},\frac{1}{2})$
2. (2, 1)
3. (1, 2)
4. $(\frac{1}{2},\frac{1}{4})$

Q.

The locus of the point of intersection of the tangents at the extremities of a chord of the circle $x^2+y^2=a^2$ which touches the circles $x^2+y^2-2ax=0$ passes through the point___

1. (a/2, 0)
   

2. (0, a/2)
   

3. (0, a)
   

4. (a, 0)

Q. The straight line x-2y+1=0 intersects the circle $x^2+y^2=25$ at points A and B, then the coordinates of points of intersection of tangents drawn at A and B are

1. (-25, 50)
2. (25, -50)
3. (-5, 25)
4. (5, -25)