Class 12

Math

Co-ordinate Geometry

Ellipse

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 $x_{2}+y_{2}=41$ to the ellipse $25x_{2} +16y_{2} =1$ then the angle between the two tangents is

The distance between directrix of the ellipse $(4x−8)_{2}+16y_{2}=(x+3 y+10)_{2}$ 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 $a_{2}x_{2} +b_{2}y_{2} =1$ whose eccentric angles are differ by $90_{∘}$, then

The locus of chords of contact of perpendicular tangents to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ 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