Circles Test 7...

If the centroid of an equilateral triangle is $$(1, 1)$$ and its one vertex is $$(-1, 2)$$ then the equation of its circumcircle is

Two vertices of an equilateral triangle are $$(-1, 0)$$ and $$(1, 0)$$, and its third vertex lies above the $$x$$-axis. The equation of the circumcircle of the triangle is

On the line joining the points $$A (0,4)$$ and $$B (3, 0)$$, a square $$ABCD $$ is constructed on the side of the line away from the origin. Equation of the circle having centre at $$C$$ and touching the axis of $$x$$ is

The equation of circle with origin as center and passing through the vertices of an equilateral triangle whose median is of length $$3a$$ is

The lines $$2x-3y=5$$ and $$3x-4y=7$$ are diameters of a circle of area $$154\ sq.\ units$$. The equation of the circle is-

The lines $$2x -3y=5$$ and $$3x -4y =7$$ are the diameters of a circle of area $$154$$ square units. An equation of this circle is $$(\pi = 22/7)$$

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

The equation of the  circle passing through $$(3,6)$$ and whose centre is $$(2,-1)$$ is-

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

The normal at the point $$(3, 4)$$ on a circle cuts the circle again at the point $$(1, 2)$$. Then the equation of the circle is -