Let d be the perpendicular distance from the centre of the ellipse to any tangent to the ellipe. If F1andF2 are the two foci of the ellipse, then shown that (PF1−PF2)2=4a2(1-d2b2)
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A line is drawn through a fix point P(α,β) to cut the circle x2+y2=r2 at A and B. Then PA.PB is equal to :
Find the locus of the centers of the circles x2+y2−2ax−2by+2=0 , where a and b are parameters, if the tangents from the origin to each of the circles are orthogonal.
represents a circle. The equation S(x,2)=0
gives two identical solutions: x=1
. The equation S(1,y)=0
given two solutions: y=0,2.
Find the equation of the circle.
The line 2x−y+1=0
is tangent to the circle at the point (2, 5) and the center of the circle lies on x−2y=4
. Then find the radius of the circle.
belong to a family of circles through the points (x1,y2)and(x2,y2)
prove that the ratio of the length of the tangents from any point on C1
to the circles C2andC3
The lengths of the tangents from P(1,−1)
to a circle are 2
, respectively. Then, find the length of the tangent from R(−1,−5)
to the same circle.
Two circles C1
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˙
Find the equation of the circle having center at (2,3) and which touches x+y=1