The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax + by + c = 0 and
bx – ay + d = 0 is r2, is a circle of radius.
The given lines are perpendicular. So shifting the origin to their point to intersection if (h, k) are the new coordinates of any point on the locus then h2 + k2 = r2 and the locus is x2 + y2 = r2 which is a circle of radius r.
If four distinct points (2, 3), (0, 2), (4, 5) and (0, t) are concylic, then t3+ 17 is equal to
Equation of a tangent to the circle with centre (2, –1) is 3x + y = 0. The squar of the length of the tangent to the circle from the point (23, 17) is
The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid-point of the line segment joining the centres of C1 and C2 and C be a circle touching C1 and C2externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C1, then the radius of the circle C is
An equation of the circle through (1, 1) and the points of intersection ofx2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is
The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0, and their ordinates are the roots of the equation x2 + 2px –q2 = 0. The radius of the circle with AB as diameter is
The locus of the point of intersection of the tangent to the circle x = r cos θ, y = r sin θ at points whose parametric angles differ by
The locus of a point which moves such that the tangents from it to the two circles x2 + y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is
If the two circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g1x + 2f1y = 0 touch each other, then
If two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 cut the coordinates axes in concyclic points, then
The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (a, b) and the coordinates axis is a