Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the equation of the parabola with vertex at origin, symmetric with respect to y-axis and passing through $(2,−3)$

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Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$16x_{2} −9y_{2} =1$

Find the equations of the hyperbola satisfying the given conditions :Foci $(0,±10 )$, passing through (2,3)

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

If $O$ is the origin and if the coordinates of any two points $Q_{1}andQ_{2}$ are $(x_{1},y_{1})and(x_{2},y_{2}),$ respectively, prove that $OQ_{1}O˙Q_{2}cos∠Q_{1}OQ_{2}=x_{1}x_{2}+y_{1}y_{2}˙$

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$x_{2}=−9y$

Find the equation of the circle with centre : (1, 1) and radius $2 $

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

If two equal chords of a circle intersect within the circle, prove that the linejoining the point of intersection to the centre makes equal angles with the chords.