R D Sharma Solutions for Chapter: The Circle, Exercise 1: EXERCISE 24.1

Find the equation of the circle with:

Centre $(a, b)$ and radius $\sqrt{a^2+b^2}$.

Find the equation of the circle with:

Centre $(a \cos \alpha , a \sin \alpha )$ and radius $a$.

Find the equation of the circle which touches both the axes and whose centre lies on $x-2y=3$ in the third quadrant.

A circle whose centre is the point of intersection of the lines $2x-3y+4=0$ and $3x+4y-5=0$ passes through the origin. Find its equation.

If the lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area $154$ square units, then obtain the equation of the circle.

Find the equation of the circle having $(1,-2)$ as its centre and passing through the intersection of the lines $3x+y=14$ and $2x+5y=18$.

One diameter of the circle circumscribing the rectangle $ABCD$ is $4y=x+7$. If the coordinates of $A$ and $B$ are $(-3, 4)$ and $(5, 4)$ respectively, find the equation of the circle.

If the line $2x-y+1=0$ touches the circle at the point $(2, 5)$and the centre of the circle lies on the line $x+y-9=0$. Find the equation of the circle.