Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the sum of the focal distances of any point on the ellipse $9x_{2}+16y_{2}=144.$

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Find the equation for the ellipse that satisfies the given conditions:Length of minor axis 16, foci $(0,±6)$.

The three points $(−2,2)(9,−2),and(−4,−3)$ are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x_{2}+4y_{2}=36$.

Does the point $(2,5),(3,5)$ lie inside, outside or on the circle $x_{2}+y_{2}=25$?

If two equal chords of a circle intersect within the circle, prove that the linejoining the point of intersection to the centre makes equal angles with the chords.

For what value of $k$ are the points $(k,2−2k),(−k+1,2k)and(−4−k,6−2k)$ collinear?

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

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