Class 12

Math

3D Geometry

Conic Sections

Find the locus of the foot of perpendicular from the point (2, 1) on the variable line passing through the point (0, 0).

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Find the equation for the ellipse that satisfies the given conditions:Length of major axis 26, foci $(±5,0)$

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 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.$4x_{2}+9y_{2}=36$

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 $AD˙$

Find the equation for the ellipse that satisfies the given conditions:Vertices $(±5,0)$, foci $(±4,0)$

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80_{∘}$, then $∠POA$ is equal to

Find the equation of the circle with centre :(0, 2) and radius 2