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
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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?
Tangents are drawn from any point on the circle x2+y2=41 to the ellipse 25x2+16y2=1 then the angle between the two tangents is
The distance between directrix of the ellipse (4x−8)2+16y2=(x+3y+10)2 is
If the normal at any point P on the ellipse cuts the major and mirror axes in G and g respectively and C be the centre of the ellipse, then
P and Q are two points on the ellipse a2x2+b2y2=1 whose eccentric angles are differ by 90∘, then
The locus of chords of contact of perpendicular tangents to the ellipse a2x2+b2y2=1 touch another fixed ellipse is
If A and B are foci of ellipse (x−2y+3)2+(8x+4y+4)2=20 andP is any point on it, then PA+PB=
An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x+2y−1=0 is a tangent to the ellipse, then the equation of the ellipse is