Find the locus of the middle points of all chords of 4x2+9y2=1 which are at a distance of 2 units from the vertex of parabola y2=−8ax˙
The range of parameter ′a′ for which the variable line y=2x+a lies between the circles x2+y2−2x−2y+1=0 and x2+y2−16x−2y+61=0 without intersecting or touching either circle is a∈(25−15,0) a∈(−∞,25−15,) a∈(0,−5−1) (d) a∈(−5−1,∞)
The chords of contact of tangents from three points A,BandC to the circle x2+y2=a2 are concurrent. Then A,BandC will (a)be concyclic (b) be collinear (c)form the vertices of a triangle (d)none of these
If the lines x+y=6andx+2y=4 are diameters of the circle which passes through the point (2, 6), then find its equation.
C1 and C2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C3 is a circle of unit radius. It passes through the centers of the circles C1andC2 and has its center above the x-axis. Find the equation of the common tangent to C1andC3 which does not pass through C2˙
Consider the circles x2+(y−1)2=9,(x−1)2+y2=25. They are such that these circles touch each other one of these circles lies entirely inside the other each of these circles lies outside the other they intersect at two points.