Locus of the mid-points to the chords of the circle x2 + y2 = 4 which subtend a right angle at the centre is
x2 + y2 = 2
Let O be the centre of the circle x2 + y2 = 4, and let AB be a chord of this circle, so that . Let M (h, k) be the mid-point of AB. ThenOM is perpendicular to AB (Fig).
Therefore, the locus of (h, k) is x2 + y2 = 2.
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
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
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