Class 11

Math

Co-ordinate Geometry

Conic Sections

If $PSQ$ is a focal chord of the ellipse $16x_{2}+25y_{2}=400$ such that $SP=8,$ then find the length of $SQ.$ is (a) $21 $ (b) $94 $ (c) $98 $ (d) $916 $

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A straight line is drawn through $P(3,4)$ to meet the axis of $x$ and $y$ at $AandB$ , respectively. If the rectangle $OACB$ is completed, then find the locus of $C˙$

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$5y_{2}−9x_{2}=36$

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.$16x_{2} +9y_{2} =1$

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

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

Find the equation of the ellipse, whose length of the major axis is 20 and foci are $(0,±5)$.

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle