Chord of Contact

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.

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.

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. 

Q. The locus of the mid points of the chord of the circle $x^2+y^2=4$, which subtended a right angle at the origin is

1. $x+y=2$
2. $x^2+y^2=2$
3. $x^2+y^2=1$
4. $x+y=1$

Q. Length of the chord of contact of (2, 5) with respect to $y^2=8x$ is

Q. Prove that the length of the chord joining the points of contact of tangents drawn from the point $(x_1,y_1)$ is $\frac{\sqrt{y_1^2+4a^2}\sqrt{y_1^2-4a{x}_1}}{a}.$

Q. In the figure $\left(i\right)$ given below, $P$ is the point of intersection of the chords $BC$ and $AQ$ such that $AB=AP$. Prove that $CP=CQ$

Q. Locus of mid points of the chords of the parabola $y^2=4ax$ which touch the circle $x^2+y^2=a^2$ is

1. $(y^2-2ax{)}^2=a^4(y^2+4a^2)$
2. $(y^2-2ax{)}^2=a^2(y^2+4a^2)$
3. $(y^2-2ax{)}^2=4a^2(y^2+4a^2)$
4. $(y^2-2ax{)}^2=2a^4(y^2+4a^2)$

Q. Locus of the mid point of the chord of circle $x^2+y^2=16$ which is subtending right angle at the point (5, 0) is

1. $x^2+y^2+4x+5/2=0$
2. $x^2+y^2-5x+9/2=0$
3. $x^2+y^2+5x+7=0$
4. $x^2+y^2+2x+5=0$

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. The equation of the circle described on the chord $3x+y+5=0$ of the circle $x^2+y^2=16$ as diameter is :

1. $x^2+y^2+3x+y-11=0$
2. $x^2+y^2+3x+y+1=0$
3. $x^2+y^2+3x+y-22=0$
4. $x^2+y^2+3x+y-2=0$

Q. If x , y , R , then solve the equation :
$(3y^2+1)lo{g}_{3}x=1$