Class 12

Math

Co-ordinate Geometry

Ellipse

If $(x,y)$ lies on the ellipse $x_{2}+2y_{3}=2$, then maximum value of $x_{2}+y_{2}+2 xy−1$ is

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A point P moves on x-y plane such that $PS+PS_{′}=4$ where $S(K,0)$ and $S_{′}(−0K,0),$ then which of the following is not true about the locus of P?

If the eccentric angles of two points P and Q on the ellipse $28x_{2} +7y_{2} =1$ whose center is C, differ by a right angle, then the area of $ΔCPQ$ is

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

Coordinates of the vertices B and C of a triangle ABC are (2,0) and (8,0) respectively. The vertex A is varying in such a way that $4tan.2B .tan.2C =1$. Then locus of A is

The value of $λ$, for which the line $2x−38 λy=−3$ is a normal to the conic $x_{2}+4y_{2} =1$ is

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

If $ω$ is one of the angles between the normals to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at the points whose eccentric angles are $θ$ and $2π +θ$, then $sin2θ2cotω $ is

The maximum distance of the centre of the ellipse $16x_{2} +9y_{2} =1$ from the chord of contact of mutually perpendicular tangents of the ellipse is