Circles Test 2...

The equation of the circle which passes through the point (3,-2) and (-2,0) and centre line 2x-y=3,is 

A circle has radius $$3$$ units and its centre lies on the line $$y=x-1$$. Then the equation of this circle if it passes through the point $$(7, 3)$$, is?

The eq. of the circle which touches the exes of y at a distance of $$4$$ from the origin and cuts the intercepts of $$6$$ units from the axis of x is

The equation of the circle having as a diameter, the chord $$x - y - 1 = 0$$ of the circle $$2x^2 + 2y^2 - 2x - 6y - 25 = 0$$, is

Let $$P,\ Q,\ R,\ S$$ be the feet of perpendicular drawn from the point $$(1,\ 1)$$ the lines $$y=3x+4$$ and $$y=-3x+6$$ and their angle bisectors respectively, the equation of the circle whose extremities of a diameter are $$R$$ and $$S$$ is 

The intercept on the line $$y = x$$ by the circle $${x^2} + {y^2} - 2x = 0$$ is $$AB$$. The equation of the circle with $$AB$$ as a diameter, is

The equation of the circle passing through the points of intersection of the lines $$2x+y=0,\ x+y+3=0$$ and $$x-2y=0$$ is

Let  $$A B C$$  be a triangle, from vertices  $$A , B$$  and  $$C$$  altitudes  $$A D , B E$$ and  $$C F$$  are drawn to opposite sides  $$B C , C A$$  and  $$A B$$  respectively which meet at a point  $$O.$$  Now triangle  $$DEF$$  is completed, also length  $$OA, OB$$  and  $$OC$$  respectively are  $$p , q$$  and  $$r.$$
Radius of the circumcircle of  $$\Delta DEF$$  is

Let $$C_1$$ and $$C_2$$ are circles defined by $$x^2+y^2-20x+64=0$$ and $$x^2+y^2+30x+144=0$$. The length of the shortest line segment PQ that is tangent to $$C_1$$ at P and to $$C_2$$ at Q is?

The value of c for which $$x+y=2$$ touches circle $$x^2+y^2-2cx=0$$ and $$(1, 0)$$ lies inside the circle, is?