Two Rods Of Lengths a and b slide Along The x-axid And y-axis Respectively In Such A Manner That Their Ends Are Concyclic. The Locus Of The Centre Of The Circle Passing Through The End Points Is

Equation of a circle through the origin and belonging to the co-axial system, of which the limiting points are (1, 2), (4, 3) is

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x² + y² = a², the locus of M is

If common chord of the circle C with centre at (2, 1) and radius r and the circle x² + y² – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is  

Tangents drawn from the point P(1, 8) to the circle x² + y² – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

An equilateral triangle is inscribed in the circle x² + y² = a² with the vertex at (a, 0). The equation of the side opposite to this vertex 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 (π = 22/7)

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

A line is drawn through the point P(3, 11) to cut the circle x² + y² = 9 at A and B. Then PA. PB is equal to

If the point (1, 4) lies inside the circle x² + y² – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then