class 11

Math

Co-ordinate Geometry

Conic Sections

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $9x_{2} +5y_{2} =1$, is:

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In $ABC$ Prove that $AB_{2}+AC_{2}=2(AO_{2}+BO_{2})$ , where $O$ is the middle point of $BC$

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 focus of a parabolic mirror as shown in is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2).

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$y_{2}=12x$ $x_{2}=−16y$$y_{2}=10x$

Find the equation of the ellipse, with major axis along the x-axis and passing through the points $(4,3)$and $(−1,4)$.

Find the equations of the hyperbola satisfying the given conditions :Foci $(±4,0)$, the latus rectum is of length 12

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$49y_{2}−16x_{2}=784$