Q. Find the equation of a circle with centre $(2,2)$ and passes through the point $(4,5)$.

Q. Find the centre and radius of the circle $(x+5){}^2+(y-3){}^2=36$

Q. Find the equation of the circle with centre $(1,1)$ and radius $\sqrt{2}$

Q. Find the center and radius of the circle $x^2+y^2-4x-8y-45=0$

Q. Find the equation of the circle passing through the points $(4,1)$ and $(6,5)$ and whose centre is on the line $4x+y=16$

Q. Find the equation of the circle with centre $(\frac{1}{2},\frac{1}{4})$ and radius $\frac{1}{12}$

Q. Find the equation of the circle passing through $(0,0)$ and making intercepts $a$ and $b$ on the coordinate axes.

Q. Find the equation of the circle with centre $(0,2)$ and radius $2$

Q. Find the equation of the circle passing through the points $(2,3)$ and $(-1,1)$ and whose centre is on the line $x-3y-11=0$

Q. Find the centre and radius of the circle $2x^2+2y^2-x=0$

Q. Find the equation of the circle with centre $(-2,3)$ and radius $4$

Q. Find the centre and radius of the circle $x^2+y^2-8x+10y-12=0$

Q. Find the equation of the circle with centre $(-a,-b)$ and radius $\sqrt{a^2-b^2}$

Q. Find the equation of the circle with radius $5$ whose centre lies on $x$-axis and passes through the point $(2,3)$

Q. Does the point $(-2.5,3.5)$ lie inside outside or on the circle $x^2+y^2=25$?

Q. Find the coordinates of the focus, axis of the parabola , the equation of directrix and the length of the latus reactum for $x$ ${}^2=6y$

Q. Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for y${}^2=10x$

Q. Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the rectum for $y^2=12x$

Q. Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola $x{}^2$ $=-16y$.

Q. Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for $y{}^2$$=-8x$