Equation of a Chord with a Given Middle Point

Q.

The locus of the centre of the circle for which one end of a diameter is $\left(1,1\right)$ while the other end is in the line $x+y=3$ is

1. $x+y=1$

2. $2\left(x-y\right)=5$

3. $2x+2y=5$

4. None of these

Q. Multiply the binomials
(i) $(2x+5)$ and $(4x-3)$

Q. The equation to the locus of the midpoints of chords of the circle $x^2+y^2=r^2$ having a constant length 2l is

1. 
2. 
3. 
4. 

Q. If the circle passing through the points $(0,0),(0,1)and(1,0)$ also passes through the point $(\lambda ,\frac{1}{\lambda })$ then $\lambda$ is

1. $1$
2. $-2$
3. $-1$
4. $2$

Q.

The circle $x^2+y^2-6x-4y+9=0$ bisects the circumference of the circle $x^2+y^2-(\lambda +4)x-(\lambda +2)y+(5\lambda +3)=0if\lambda$ is equal to

1. -1
   

2. 1
   

3. 2
   

4. 4