For an ellipse 9x2+4y2=1 with vertices A and A', drawn at the point P in the first quadrant meets the y axis in Q and the chord A'P meets the y axis in M. If 'O' is the origin then OQ2−MQ2
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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 area of the triangle formed by the lines joining the vertex of the parabola x2=12yto the ends of its latus rectum.
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.
The coordinates of the point AandB
are (a,0) and (−a,0),
respectively. If a point P
moves so that PA2−PB2=2k2,
is constant, then find the equation to the locus of the point P˙
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Find the equation of the hyperbola where foci are (0,±12)and the length of the latus rectum is 36.
Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.5y2−9x2=36
Find the coordinates of the circumcenter of the triangle whose vertices are (A(5,−1),B(−1,5),
Find its radius also.