Class 11

Math

Co-ordinate Geometry

Conic Sections

Prove that any point on the ellipse whose foci are $(−1,0)$ and $(7,0)$ and eccentricity is $21 $ is $(3+8cosθ,43 sinθ),θ∈R˙$

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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.$36x_{2} +16y_{2} =1$

In any triangle ABC, if the angle bisector of $∠A$and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

Find the locus of a point, so that the join of $(−5,1)$ and $(3,2)$ subtends a right angle at the moving point.

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Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line $4x+y=16$.

Find the area of a triangle having vertices $A(3,2),B(11,8),$ and $C(8,12)˙$