Class 11

Math

Co-ordinate Geometry

Conic Sections

An ellipse slides between two perpendicular straight lines. Then identify the locus of its center.

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Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$y_{2}=−8x$

Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0), passing through (5, 2) and symmetric with respect to y–axis.

Find the coordinates of the point which divides the line segments joining the points $(6,3)$ and $(−4,5)$ in the ratio $3:2$ (i) internally and (ii) externally.

Find the equation for the ellipse that satisfies the given conditions:Vertices $(±6,0)$, foci $(±4,0)$

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$49y_{2}−16x_{2}=784$

An arch is in the form of a semi–ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Find the equation of the circle with centre :$(21 ,41 )$ and radius $121 $

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.