Orthogonality of Two Circles

Q.

Find the equation of the circle which passes through the origin and has its center on the line $x+y+4=0$ and cuts the circle $x^2+y^2-4x+2y+4=0$ orthogonally.

1. $3x^2+3y^2+20x+4y=0$

2. $x^2+y^2+4x+20y=0$

3. $3x^2+3y^2-4x+20y=0$

4. $x^2+y^2+20x+4y=0$

Q.

If two circles which pass through the points (0, a) and (0, -a) cut each other orthogonally and touch the straight line $y=mx+c$, then

1. $c^2=a^2(1+m^2)$
2. $c^2=a^2|1+m^2|$
3. $c^2=2a^2(1+m^2)$
4. $c^2=a^2(2+m^2)$

Q. The centre and radius of the circle passing through the points $(1,0),(3,-2)$ and $(-1,-2)$ are given by

1. $(1,-2);2$
2. $(1,2);2$
3. $(-1,-2);1$
4. $(-1,2);1$