Class 11

Math

Co-ordinate Geometry

Conic Sections

The center of an ellipse is $C$ and $PN$ is any ordinate. Point $A,A_{′}$ are the endpoints of the major axis. Then find the value of $ANPN_{2} A˙_{prime}N˙$

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Find the equation for the ellipse that satisfies the given conditions:Major axis on the x–axis and passes through the points (4, 3) and (6, 2).

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.$36x_{2} +16y_{2} =1$

The sum of the squares of the distances of a moving point from two fixed points (a,0) and $(−a,0)$ is equal to a constant quantity $2c_{2}˙$ Find the equation to its locus.

Find the area of the pentagon whose vertices are $A(1,1),B(7,21),C(7,−3),D(12,2),$ and $E(0,−3)$

The line joining the points $(x,2x)and(3,5)$ makes an obtuse angle with the positive direction of the x-axis. Then find the values of $x˙$

Find the equation of the circle with centre (–3, 2) and radius 4.

The coordinates of the point $AandB$ are (a,0) and $(−a,0),$ respectively. If a point $P$ moves so that $PA_{2}−PB_{2}=2k_{2},$ when $k$ is constant, then find the equation to the locus of the point $P˙$

The vertices of a triangle are $A(x_{1},x_{1},tanθ_{1}),B(x_{2},x_{2},tanθ_{2})$ and $C(x_{3},x_{3},tanθ_{3})$. If the circumcentre coincides with origin then