Equation Of The Circle Which Passes Through The Origin, Has Its Centre On The Line x + y = 4 And Cuts The Circle X2 + y2 – 4x + 2y + 4 = 0 Orthogonally, Is

Locus of the mid-points to the chords of the circle x² + y² = 4 which subtend a right angle at the centre is

A circle C touches the x-axis and the circle x² + (y – 1)² = 1externally, then locus of the centre of the circle is given by

Three circles with radii 3 cm, 4 cm and 5 cm touch each other externally. If A is the point of intersection of tangents to these circles at their points of contact, then the distance of A from the points of contact is

A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is

If a circle passes through the point (a, b) and cuts the circle x² + y² = k² orthogonally, equation of the locus of its centre is

If O is the origin and OP, OQ are distinct tangents to the circle x² + y² + 2gx + 2fy + c = 0, the circumcentre of the triangle OPQ is

The circle passing through the distinct points (1, t), (t, 1) and (t, t) for all values of t, passes through the point

If OA and OB are the tangents from the origin to the circle x² + y² + 2gx + 2fy + c = 0, and C is the centre of the circle, the area of the quadrilateral OACB is 

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x – 6y + 9 sin²α + 13 cos²α = 0 is 2α. The equation of the locus of the point P 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