If the normal at one end of the latus rectum of the ellipse a2x2+b2y2=1 passes through one end of the minor axis, then prove that eccentricity is constant.
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Find the angle between the two tangents from the origin to the circle (x−7)2+(y+1)2=25
Tangent drawn from the point P(4,0)
to the circle x2+y2=8
touches it at the point A
in the first quadrant. Find the coordinates of another point B
on the circle such that AB=4
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
If the distances from the origin of the centers of three circles x2+y2+2λx−c2=0,(i=1,2,3),
are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle x2+y2=c2
are in GP.
If the circle x2+y2+2gx+2fy+c=0
bisects the circumference of the circle x2+y2+2gprimex+2fprimey+cprime=0
then prove that
are drawn to x2+y2=a2
from the point P(x1,y1)˙
Then find the equation of the circumcircle of triangle PAB˙
Find the equations to the common tangents of the circles x2+y2−2x−6y+9=0 and x2+y2+6x−2y+1=0
Find the equation of the circle whose radius is 3 and which touches internally the circle x2+y2−4x−6y=−12=0
at the point (−1,−1)˙