From a point P perpendicular tangents PQ and PR are drawn to ellipse x2+4y2=4, then locus of circumcentre of triangle PQR is
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If (x,y) lies on the ellipse x2+2y3=2, then maximum value of x2+y2+2xy−1 is
The foci of an ellipse are (−2,4) and (2,1). The point (1,623) is an extremity of the minor axis. What is the value of the eccentricity?
the eccentricity of the locus of the locus of point (3h+2,k), where (h,k) lies on the ellipse x2+y2=1, is
The length of the major axis of the ellipse (5x−10)2+(5y+15)2=4(3x−4y+7)2 is
Find the equation of chord of an ellipse 25x2+16y2=1 joining two points P(3π)andQ(6π)
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)
PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R are 2α,2β,2γ, respectively then tanβγ is equal to
If the normal at any point P on the ellipse a2x2+b2y2=1 meets the axes at G and g, respectively, then find the ratio PG :Pg