ELLIPSE | Part 1

ELLIPSE : Basic OF ellipse || Different form OF ellipse || Eccentric angles and Auxiliary circle || Latus rectum

A circle touches the line L and the circle C_(1) externally such that both the circles are on the same side of the line,then the locus of centre of the circle is (a) Ellipse (b) Hyperbola (c) Parabola (d) Parts of straight line

The locus of mid points of parts in between axes and tangents of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 will be

The diameter of the largest circle with center (1,0) which is inscribed in the ellipse x^(2)+4y^(2)=16 is k.Then integral part of k is

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

If F_1 (-3, 4) and F_2 (2, 5) are the foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

The ends of the major axis of an ellipse are (-2,4) and (2,1) .If the point (1,3) lies on the ellipse,then find its latus rectum and eccentricity.

For all real p, the line 2px+ysqrt(1-p^(2))=1 touches a fixed ellipse whose axex are the coordinate axes The foci of the ellipse are

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :