R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

Find the equation of the circle concentric with the circle $x^2+y^2-4x-6y-3=0$ and which touches the $y-$axis.

Find the equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and of double its area.

Prove that the centres of the three circles $x^2+y^2-4x-6y-12=0$,$x^2+y^2+2x+4y-5=0$ and $x^2+y^2-10x-16y+7=0$ are collinear.

Find the equation of the circle which passes through the points $A(1,1)$ and $B(2,2)$ and whose radius is $1$ Show that there are two such circles.

Find the equation of a circle passing through the origin and intercepting lengths $a$ and $b$ on the axes.

Find the equation of the circle circumscribing the triangle formed by the lines $x+y=6, 2x+y=4$ and $x+2y=5$.

Show that the quadrilateral formed by the straight lines $x-y=0,3x+2y=5$,$x-y=10$ and $2x+3y=0$ is cyclic and hence find the equation of the circle.

If $(-1,3)$ and $(\alpha ,\beta )$ are the extremities of the diameter of the circle $x^2+y^2-6x+5y-7=0$, find the coordinates $(\alpha ,\beta )$.