Find the eccentric angles of the extremities of the latus recta of the ellipse a2x2+b2y2=1
A tangent is drawn to each of the circles x2+y2=a2 and x2+y2=b2˙ Show that if the two tangents are mutually perpendicular, the locus of their point of intersection is a circle concentric with the given circles.
AandB are two points in the xy-plane, which are 22 units distance apart and subtend an angle of 900 at the point C(1,2) on the line x−y+1=0 , which is larger than any angle subtended by the line segment AB at any other point on the line. Find the equation(s) of the circle through the points A,BandC˙
An infinite number of tangents can be drawn from (1,2) to the circle x2+y2−2x−4y+λ=0 . Then find the value of λ
Find the equations of the circles passing through the point (−4,3) and touching the lines x+y=2 and x−y=2
Find the equation of the tangent at the endpoints of the diameter of circle (x−a)2+(y−b)2=r2 which is inclined at an angle θ with the positive x-axis.
Two circles C1 and C2 intersect in such a way that their common chord is of maximum length. The center of C1 is (1, 2) and its radius is 3 units. The radius of C2 is 5 units. If the slope of the common chord is 43, then find the center of C2˙