Find the equation of chord of an ellipse 25x2+16y2=1 joining two points P(3π)andQ(6π)
If the intercepts of the variable circle on the x- and yl-axis are 2 units and 4 units, respectively, then find the locus of the center of the variable circle.
Find the locus of the midpoint of the chord of the circle x2+y2−2x−2y=0 , which makes an angle of 1200 at the center.
Let P be a point on the circle x2+y2=9,Q a point on the line 7x+y+3=0 , and the perpendicular bisector of PQ be the line x−y+1=0 . Then the coordinates of P are (0,−3) (b) (0,3) (2572,3521) (d) (−2572,2521)
Statement 1 :The circles x2+y2+2px+r=0 and x2+y2+2qy+r=0 touch if p21+q21=e1˙ Statement 2 : Two centers C1andC2 and radii r1andr2, respectively, touch each other if ∣r1±r2∣=c1c2˙
Find the length of the chord of contact with respect to the point on the director circle of circle x2+y2+2ax−2by+a2−b2=0 .
Consider three circles C1,C2andC3 such that C2 is the director circle of C1,andC3 is the director circlÃ© of C2. Tangents to C1, from any point on C3 intersect C2, at P2andQ. Find the angle between the tangents to C22 at P and Q. Also identify the locus of the point of intersec- tion of tangents at PandQ.