Diameter Form of a Circle

Write the coordinates of the centre of the circle inscribed in the square formed by the lines $x=2, x=6, y=5$ and $y=9$.

Write the equation of the circle passing through $(3,4)$ and touching $y$-axis at the origin.

If the abscissae and ordinates of two points $P$ and $Q$ are roots of the equations $x^2+2ax-b^2=0$ and $x^2+2px-q^2=0$ respectively, then write the equation of the circle with $PQ$ as diameter.

Write the coordinates of the centre of the circle passing through $(0,0), (4,0)$ and $(0,-6)$

If the equation of the unit circle concentric with $x^2+y^2-8x+4y-8=0$ is $x^2+y^2+2gx+2fy+c=0$, then find the value of $c$.

If the area of the circle passing through $(-2,6)$ and having its centre at $(1,2)$ is $k\pi$ square units, then find the value of $k$.

Find the equation of the circle which circumscribes the triangle formed by the lines $x=0, y=0 and lx+my=1$.

The line  $2x-y+6=0$ meets the circle $x^2+y^2-2y-9=0$ at $A$ and $B$. Find the equation of the circle on $AB$as diameter. 

$ABCD$ is a square whose side is $a;$ taking  $A\mathrm{B }$and $AD$ as axes, prove that the equation of the circle circumscribing the square is $x^2+y^2-a(x+y)=0$

The abscissae of the two points $A$ and $B$ are the roots of the equation $x^2+2ax-b^2=0$ and their ordinates are the roots of the equation  $x^2+2px-q^2=0$. Find the equation of the circle with $AB$ as diameter. Also, find its radius.

Find the equation of the circle whose diameter is the line segment joining $(-4,3)$and $(12,-1) .$ Find also the intercept made by it on $y$ -axis.

Find the equation of the circle which passes through the origin and cuts off intercepts $a$ and $b$ respectively from$x$ and $y$-axes.

Find the equation of the circle passing through the origin and the points where the line $3x+4y=12$  meets the axes of coordinates.

Find the equation of the circle circumscribing the rectangle whose sides are :  $x-3y=4,$ $3x+y=22, x-3y=14$ and $3x+y=62$.

The sides of a square are $x=6, x=9, y=3$ and $y=6.$ Find the equation of a circle drawn on the diagonal of the square as its diameter.

Find the equation of the circle the end points of whose diameter are the centres of the circles $x^2+y^2+6x-14y-1=0\text{ and }{x}^2+y^2-4x+10y-2=0$

Find the equation of the circle, the end points of whose diameter are$(2,-3)$ and $(-2,4)$ Find its centre and radius.

If the line $y=mx$ does not intersect the circle $(x+10{)}^2+(y+10{)}^2=180$, then write the set of values taken by $m$

If the radius of the circle $x^2+y^2+ax+(1-a)y+5=0$ does not exceed $5$, write the number of integral values $a$.

If the length of the intercept made by the circle $x^2+y^2+2x-4y-5=0$ on $y$ -axis is $l \mathrm{units}$, find the value of $l$.