Director Circle

Q. If a circle whose centre is (1, -3) touches the line 3x-4y-5=0, then the radius of the circle is

1. 2

2. 4

3. 

4. 

Q. The equation of the tangent to the circle $x^2+y^2$ + 4x - 4y + 4 = 0 which make equal intercepts on the positive coordinates, is

1. x + y = 2
2. x + y =
3. x + y = 2
4. none

Q.

A set of parallel chords of the parabola $y^2=4ax$ have their mid points on

1. any straight line through the vertex

2. any straight line through the focus

3. a straight line parallel to the axis

4. another parabola

Q. Which of the following represents the
director circle for the parabola $y^2=4ax?$

1. $x^2+y^2=a^2$
2. $x^2+y^2=1$
3. $x+a=0$

4. $x=a$

Q.

The chord AB of the parabola $y^2=4ax$ cuts the axis of the parabola at C. If $A=(a{t}_1^2,2a{t}_1),B=(a{t}_2^2,2a{t}_2)$ and AC : AB = 1:3 then

1. $t_2=2t_1$

2. $t_2+2t_1=0$

3. $t_1+2t_2=0$

4. None of these

Q.

Find the equation of director circle of the circle $(x-1{)}^2+(y-2{)}^2=4$

1. $(x-1{)}^2+(y-2{)}^2=4\sqrt{2}$

2. $(x-1{)}^2+(y-2{)}^2=8$

3. $(x+1{)}^2+(y+2{)}^2=4\sqrt{2}$

4. $(x-2{)}^2+(y-1{)}^2=8$