The equation of the circle which touches the axis of y at the origin and passes through (3, 4) is
The equation to the circle whose radius is 4 and which touches the negative xaxis at a distance 3 units from the origin is
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Number of different circles that can be drawn touching 3 lines, no two of which are parallel and they are neither coincident nor concurrent, are
If a circle of constant radius 3k passes through the origin `O' and meets coordinate axes at A and B then the locus of the centroid of the triangle OAB is
A pair of tangents are drawn from the origin to the circle x^{2} + y^{2} + 20(x + y) + 20 = 0. The equation of the pair of tangents is
The locus of the centre of a circle which touches externally the circle, x^{2} + y^{2} – 6x – 6y + 14 = 0 and also touches the yaxis is given by the equation
The common chord of two intersecting circles C_{1} and C_{2} can be seen from their centres at the angles of 90º and 60º respectively. If the distance between their centres is equal to √3 + 1 then the radius of C_{1} and C_{2} are
A circle touches a straight line lx + my + n = 0 and cuts the circle x^{2} + y^{2} = 9 orthogonally, The locus of centres of such circles is
The length of the common chord of circles x^{2} + y^{2} – 6x – 16 = 0 and x^{2} + y^{2} – 8y – 9 = 0 is
If the two circles, x^{2} + y^{2} + 2g_{1}x + 2f_{1}y = 0 and x^{2} + y^{2} + 2g_{2}x + 2f_{2}y = 0 touches each other, then
If , , & are four distinct points on a circle of radius 4 units then, abcd =
What is the length of shortest path by which one can go from (–2, 0) to (2, 0) without entering the interior of circle, x^{2} + y^{2} = 1
Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circle internally is
In a right triangle ABC, right angled at A, on the leg AC as diameter, a semicircle is described. The chord joining A with the point of intersection D of the hypotenuse and the semicircle, then the length AC equals to
The circle passing through the distinct points (1, t), (t, 1) & (t, t) for all values of `t'. passes through the point
The locus of the mid points of the chords of the circle x^{2} + y^{2} – ax – by = 0 which subtend a right angle at is
A circle is inscribed into a rhombus ABCD with one angle 60º. The distance from the centre of the circle to the nearest vertex is equal to 1. If P is any point of the circle, then  PA ^{2} +  PB ^{2} +  PC ^{2} +  PD ^{2} is equal to
Number of points (x, y) having integral coordinates satisfying the condition x^{2} + y^{2} < 25 is
Circles are drawn touching the coordinate axis and having radius 2, then
For the circles S_{1} º x^{2} + y^{2} – 4x – 6y – 12 = 0 and S_{2} º x^{2} + y^{2} + 6x + 4y – 12 = 0 and the line L º x + y = 0
x^{2} + y^{2} + 6x = 0 and x^{2} + y^{2}  2x = 0 are two circles, then
3 circle of radii 1, 2 and 3 and centres at A, B and C respectively, touch each other. Another circle whose centre is P touches all these 3 circles externally. and has radius r. Also ∠PAB = q & ∠PAC = a.
Slope of tangent to the circle (x – r)^{2} + y^{2} = r^{2} at the point (x, y) lying on the circle is
The centre(s) of the circle(s) passing through the points (0, 0), (1, 0) and touching the circle x^{2} + y^{2} = 9 is/are
Point M moved along the circle (x – 4)^{2} + (y – 8)^{2} = 20. Then it broke away from it and moving along a tangent to the circle cuts the xaxis at the point (–2, 0). The coordinates of the point on the circle at which the moving point broke away can be
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447 docs930 tests
