If the pair of lines $$a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
A
$$3{a^2} - 10ab + 3{b^2} = 0$$
B
$$3{a^2} - 2ab + 3{b^2} = 0$$
C
$$3{a^2} + 10ab + 3{b^2} = 0$$
D
$$3{a^2} + 2ab + 3{b^2} = 0$$
Explanation
As per question area of one sector $$=3$$ area of another sector
$$ \Rightarrow $$ at center by one sector $$ = 3 \times $$ angle at center by another sector
If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0$$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
A
exactly one value of a
B
no value of a
C
infinitely many values of a
D
exactly two values of a
Explanation
$${s_1} = {x^2} + {y^2} + 2ax + cy + a = 0$$
$${s_2} = {x^2} + {y^2} - 3ax + dy - 1 = 0$$
Equation of common chord of circles $${s_1}$$ and $${s_2}$$ is
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = {p^2}$$ orthogonally, then the equation of the locus of its centre is