Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the center, foci, the length of the axes, and the eccentricity of the ellipse $2x_{2}+3y_{2}−4x−12y+13=0$

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Find the equations of the hyperbola satisfying the given conditions :Foci $(0,±10 )$, passing through (2,3)

Find the equation of the hyperbola where foci are $(0,±12)$and the length of the latus rectum is 36.

The vertices of a triangle are $A(−1,−7),B(5,1)andC(1,4)˙$ If the internal angle bisector of $∠B$ meets the side $AC$ in $D,$ then find the length $AD˙$

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.

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

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

Find the area of the pentagon whose vertices are $A(1,1),B(7,21),C(7,−3),D(12,2),$ and $E(0,−3)$

Find the equation for the ellipse that satisfies the given conditions:Ends of major axis $(±3,0)$, ends of minor axis $(0,±2)$