Find the point on the ellipse 16x2+11y2=256 where the common tangent to it and the circle x2+y2−2x=15 touch.
Perpendiculars are drawn, respectively, from the points PandQ to the chords of contact of the points QandP with respect to a circle. Prove that the ratio of the lengths of perpendiculars is equal to the ratio of the distances of the points PandQ from the center of the circles.
The line 3x+6y=k intersects the curve 2x2+3y2=1 at points AandB . The circle on AB as diameter passes through the origin. Then the value of k2 is__________
Find the equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x2+y2=9
Statement 1 : Let S1:x2+y2−10x−12y−39=0, S2x2+y2−2x−4y+1=0 and S3:2x2+2y2−20x=24y+78=0. The radical center of these circles taken pairwise is (−2,−3)˙ Statement 2 : The point of intersection of three radical axes of three circles taken in pairs is known as the radical center.
A variable circle passes through the point A(a,b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x−a)2=4by˙
Find the number of integral values of λ for which x2+y2+λx+(1−λ)y+5=0 is the equation of a circle whose radius does not exceed 5.
If one end of the a diameter of the circle 2x2+2y2−4x−8y+2=0 is (3, 2), then find the other end of the diameter.