Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the equation of the ellipse (referred to its axes as the axes of $xandy$ , respectively) whose foci are $(±2,0)$ and eccentricity is $21 $

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Express the polar equation $r=2cosθ$ in rectangular coordinates.

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

Given that $A(1,1)$ and $B(2,−3)$ are two points and $D$ is a point on $AB$ produced such that $AD=3AB˙$ Find the coordinates of $D˙$

Find the equation of the circle passing through the points $(2,3)$and $(−1,1)$and whose centre is on the line $x−3y−11=0$.

Find the equation of the circle with centre : $(−2,3)$and radius 4

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse $25x_{2} +9y_{2} =1$

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

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