Class 12

Math

3D Geometry

Conic Sections

The line joining the points $(x,2x)and(3,5)$ makes an obtuse angle with the positive direction of the x-axis. Then find the values of $x˙$

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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 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.$36x_{2}+4y_{2}=144$

The points $(−a,−b),(a,b),(a_{2},ab)$ are (a) vertices of an equilateral triangle (b) vertices of a right angled triangle (c) vertices of an isosceles triangle (d) collinear

Find the equation of the parabola that satisfies the given conditions:Vertex (0,0) passing through (2,3) arid axis is along x–axis.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$x_{2}=−9y$

Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0); focus $(2,0)$

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

Find the locus of a point such that the sum of its distance from the points (2, 2) and $(2,−2)$ is 6.