If the tangent to the circle ${x^2} + {y^2} = {r^2}$ at the point $(a, b)$ meets the coordinate axes at the point $A$ and $B$, and $O$ is the origin, then the area of the triangle $OAB$ is

The line $(x – a)\cos \alpha + (y – b)$ $\sin \alpha = r$ will be a tangent to the circle ${(x – a)^2} + {(y – b)^2} = {r^2}$

From any point on the circle ${x^2} + {y^2} = {a^2}$ tangents are drawn to the circle ${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $, the angle between them is

The equation of the circle having the lines $y^2 – 2y + 4x – 2xy = 0$ as its normals $\&$ passing through the point $(2 , 1)$ is :

If the straight line $ax + by = 2;a,b \ne 0$ touches the circle ${x^2} + {y^2} – 2x = 3$ and is normal to the circle ${x^2} + {y^2} – 4y = 6$, then the values of a and b are respectively