Dr. SK Goyal Solutions for Chapter: Circle, Exercise 11: Multiple Choice II

If $OA$ and $OB$ are two perpendicular chords of the circle $r=a\cos \theta +b\sin \theta$ passing through origin, then the locus of the mid point of $AB$ is :

An equation of a circle touching the axes of co-ordinates and the line $x\cos \alpha +y\sin \alpha =2$ can be :

If $P$ is a point on the circle $x^2+y^2=9,Q$ is a point on the line $7x+y+3=0$ and the line $x-y+1=0$ is the perpendicular bisector of $PQ$, then the co-ordinates of $P$ are :

If a circle passes through the point $\left(3,\sqrt{\frac{7}{2}}\right)$ and touches $x+y=1$ and $x-y=1$, then the centre of the circle is :

The equations of four circles are ${\left(x\pm a\right)}^2+{\left(y\pm a\right)}^2=a^2$. The radius of a circle touching all the four circles is:

If a circle passes through the points of intersection of the co-ordinates axes with the lines $\lambda x-y+1=0$ and $x-2 y+3=0$, then the value of $\lambda$ is :

Consider the circles
$C_1\equiv x^2+y^2-2x-4y-4=0$ and $C_2\equiv x^2+y^2+2x+4y+4=0$ and the line $L\equiv x+2y+2=0$. Then

If point $P\left(x, y\right)$ is called a lattice point if $x,y\in I$. Then the total number of lattice points in the interior of the circle $x^2+y^2=a^2,a\ne 0$ can not be :