Class 11

Math

Co-ordinate Geometry

Conic Sections

If (5, 12) and (24, 7) are the foci of an ellipse passing through the origin, then find the eccentricity of the ellipse.

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

Find the equation of the hyperbola with foci $(0,±3)$and vertices $(0,±211 )$

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$x_{2}=6y$

Find the equation to which the equation $x_{2}+7xy−2y_{2}+17x−26y−60=0$ is transformed if the origin is shifted to the point $(2,−3),$ the axes remaining parallel to the original axies.

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

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Find the equation of the ellipse, with major axis along the x-axis and passing through the points $(4,3)$and $(−1,4)$.

Find the equation for the ellipse that satisfies the given conditions:b = 3, c = 4, centre at the origin; foci on a x axis.