Two Points P and Q are Taken On The Line Joining The Points A (0, 0) And B (3a, 0) Such That AP = PQ = QB. Circles Are Drawn OnAP, PQ, And QB as Diameters. The Locus Of The Point S, The Sum Of The Squares Of The Lengths Of The Tangents From Which To The Three Circles Is Equal To b2, 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

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

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

If the line x cos α + y sin α = p represents the common chord APQB of the circle x² + y² = a² and x² + y² = b² (a > b) as shown in the Fig, then AP is equal to

If OA and OB are two equal chords of the circle x² + y² – 2x + 4y = 0 perpendicular to each other and passing through the origin O, the slopes of OA and OB are the roots of the equation