A point P on the ellipse `(x^(2))/(2)+(y^(2))/(1)=1` is at distance of `sqrt(2)` from its focus s. the ratio of its distance from the directrics of the ellipse is

A point P lies on the ellipe ((y-1)^(2))/(64)+((x+2)^(2))/(49)=1 . If the distance of P from one focus is 10 units, then find its distance from other focus.

The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is

Let there are exactly two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose distance from (0, 0) are equal to sqrt((a^(2))/(2)+b^(2)) . Then, the eccentricity of the ellipse is equal to

The ecentric angle of the points on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 whose distane from its centre is 2 is/are.

If the normal to the ellipse x^2/25+y^2/1=1 is at a distance p from the origin then the maximum value of p is

There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2) =1 whose distance from the centre of the ellipse are equal to sqrt((3a^2-b^2)/(3)) . Eccentricity of this ellipse is

If two points are taken on the mirror axis of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at the same distance from the centre as the foci, then the sum of the sequares of the perpendicular distance from these points on any tangent to the ellipse is

A point on the ellipse x^(2)/16 + y^(2)/9 = 1 at a distance equal to the mean of lengths of the semi - major and semi-minor axis from the centre, is

A parabola is drawn with focus at one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. If the latus rectum of the ellipse and that of the parabola are same,then the eccentricity of the ellipse is 1-(1)/(sqrt(2)) (b) 2sqrt(2)-2sqrt(2)-1( d) none of these