Length of the latus rectum of the parabola x+y=a is
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 100x2+400y2=1.
Find the locus of the point which is such that the chord of contact of tangents drawn from it to the ellipse a2x2+b2y2=1 form a triangle of constant area with the coordinate axes.
If the normal at one end of the latus rectum of the ellipse a2x2+b2y2=1 passes through one end of the minor axis, then prove that eccentricity is constant.
Tangents are drawn to the ellipse a2x2+b2y2=1,(a>b), and the circle x2+y2=a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan−1(2aba−b) (B) tan−1(2aba+b) (C) tan−1(a−b2ab) (D) tan−1(a+b2ab)
If F1 and F2 are the feet of the perpendiculars from the foci S1andS2 of the ellipse 25x2+16y2=1 on the tangent at any point P on the ellipse, then prove that S1F1+S2F2≥8.
Tangents are drawn to the ellipse a2x2+b2y2=1 at two points whose eccentric angles are α−β and α+β The coordinates of their point of intersection are