Chord of contact

Q.

The locus of the midpoints of the chord of the circle, $x^2+y^2=25$ which is tangent to the hyperbola, $\frac{x^2}{9}-\frac{y^2}{16}=1$is

1. ${(x^2+y^2)}^2–16x^2+9y^2=0$

2. ${(x^2+y^2)}^2–9x^2+144y^2=0$

3. ${(x^2+y^2)}^2–9x^2–16y^2=0$

4. ${(x^2+y^2)}^2–9x^2+16y^2=0$

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. Let x(x - a) + y(y - 1) be a circle. If two chords from (a, 1) bisected by the x-axis are drawn to the circle then the condition required is

1. none
2. = 8
3. 8
4. 8

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. 

2. None of these

3. RQ

4. 

Q. Show that the locus of the mid-points of the chords of the circle $x^2+y^2-2x-2y-2=0$ which make an angle of ${120}^{\circ }$ at the centre is $x^2+y^2-2x-2y+1=0$.

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.

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

1. P only

2. Q Only

3. Both P and Q

4. Neither P and Q

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. -85 < m < -35

4. 35 < m < 85

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

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. -1

2. 1

3. 0

4.