Dr. SK Goyal Solutions for Chapter: Circle, Exercise 10: Multiple Choice I

The equation of a circle passing through two points $\left(1,1\right)$ and $\left(2,2\right)$ having the radius $4$ times the radius of smallest circle passing from above two points is :

Length of tangent drawn from any point of the circle $x^2+y^2+2gx+2fy+c=0$ to the circle $x^2+y^2+2gx+2fy+d=0; \left(d>c\right)$ is :

A circle circumscribing an equilateral triangle with centroid at $\left(0,0\right)$ of a side $a$ is drawn and a square is drawn touching its four sides to circle. The equation of circle circumscribing the square is:

The centre of a circle which is orthogonal to the circles $C_1:x^2+y^2=25$ and $C_2:(x-7{)}^2+(y-5{)}^2=4$ and which has the least radius is:

The equation $x^2+y^2=\left|\left|2x-2\right|+2\left|y-1\right|\right|$ represents :

The points $\left(4,-2\right)$ and $\left(3,b\right)$ are conjugate with respect to the circle $x^2+y^2=24$, if $b=$

The circle $x^2+y^2+4x-6y+9=0$ undergoes the following transformation $3 f\left(x,y\right)-f\left(x+1,y\right)+f\left(x,y+1\right)=0$ then the ratio of areas of the new circle to original circle is :

The maximum number of points with rational co-ordinates on a circle whose centre is $\left(\sqrt{3},0\right)$ is: