Class 11

Math

Co-ordinate Geometry

Conic Sections

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

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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.$25x_{2} +100y_{2} =1$

Find the equations of the hyperbola satisfying the given conditions :Vertices $(±2,0),foci(±3,0)$

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

Find the orthocentre of the triangle whose vertices are $(0,0),(3,0),$ and $(0,4)˙$

Find the equation of the parabola with focus (2, 0) and directrix $x=−2$.

Find the equation for the ellipse that satisfies the given conditions:Major axis on the x–axis and passes through the points (4, 3) and (6, 2).

Find the equation of the circle which passes through the points $(2,−2)$, and (3,4) and whose centre lies on the line $x+y=2$.

Prove that the point $(−2,−1),(1,0),(4,3)and(1,2)$ are the vertices of parallel-gram. Is it a rectangle?