Properties of Orthogonality of Two Circles

Q. Factorise $a^3(b-c)+b^3(c-a)+c^3(a-b)$

1. $-(a-b-c)(a-b)(b-c)(c-a)$
2. $-(a+b+c)(a-b)(b-c)(c-a)$
3. $(a+b+c)(a-b)(b-c)(c-a)$
4. None

Q. A circle S passes through the point (0, 1) and is orthogonal to the circles $(x-1{)}^2+y^2=16$ and $x^2+y^2=1$ then,

1. Radius of S is 8
2. Radius of S is 7
3. Centre of S is (-7, 1)
4. Center of S is (-8, 1)

Q. Two given circles $x^2+y^2+ax+by+c=0$ and $x^2+y^2+dx+ey+f=0$ will intersect each other orthogonally, only when

1. a+b+c = d+e+f
2. ad+be = c+f
3. 2ad+2be = c+f