Class 12

Math

Co-ordinate Geometry

Ellipse

From a point P perpendicular tangents PQ and PR are drawn to ellipse $x_{2}+4y_{2}=4$, then locus of circumcentre of triangle PQR is

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If $(x,y)$ lies on the ellipse $x_{2}+2y_{3}=2$, then maximum value of $x_{2}+y_{2}+2 xy−1$ 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 $x_{2}+y_{2}=1$, 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 $25x_{2} +16y_{2} =1$ 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 $F_{1}andF_{2}$ are the two foci of the ellipse, then shown that $(PF_{1}−PF_{2})_{2}=4a_{2}$(1-$d_{2}b_{2} )$

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 $a_{2}x_{2} +b_{2}y_{2} =1$ meets the axes at G and g, respectively, then find the ratio PG :Pg