Centre of the ellipse `((x-h)^(2))/(a^(2))+((y-k)^(2))/(b^(2))=1(a

Equation of the directrices of the ellipse ((x-h)^(2))/(a^(2))+((y-k)^(2))/(b^(1))=1 (a>b)

Equation of major axis of the ellipse ((x-h)^(2))/(a^(2))+((y-k)^(2))/(b^(2))=1 (a

End points of the major axis of the ellipse ((x-h)^(2))/(a^(2))+((y-k)^(2))/(b^(2))=1(a

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Let d be the perpendicular distance from the centre of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to the tangent drawn at a point P on the ellipse.If F_(1)&F_(2) are the two foci of the ellipse,then show the (PF_(1)-PF_(2))^(2)=4a^(2)[1-(b^(2))/(d^(2))]

If the area of the auxiliary circle of the ellipse (x ^(2))/(a ^(2)) + (y ^(2))/(b ^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

The value of a for the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b), if the extremities of the latus rectum of the ellipse having positive ordinates lie on the parabola x^(2)=2(y-2) is

If the locus of the middle point of the portion of a tangent of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the axes is ((a^(2))/(x^(2)))+((b^(2))/(y^(2)))=k, then the value of k is

the equation of a diameter conjugate to a diameter y=(b)/(a)x of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is