The point of intersection of the tangents at the point `P` on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and its corresponding point `Q` on the auxiliary circle meet on the line (a) `x=a/e` (b) `x=0` (c) `y=0` (d) none of these

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

The line x=at^(2) meets the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 in the real points if

Let a tangent at a point P to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets directrix at Q and S be the correspondsfocus then /_PSQ

Locus of point of intersection of perpendicular tangents to the circle x^(2)+y^(2)-4x-6y-1=0 is

P is a point on the ellipse E:x^2/a^2+y^2/b^2=1 and P' be the corresponding point on the auxiliary circle C: x^2+y^2=a^2 . The normal at P to E and at P' to C intersect on circle whose radius is

If the tangent at theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the auxiliary circle at two points which subtend a right angle at the centre then e^(2)(2-cos^(2)theta) =

The ratio of the area of triangle inscribed in ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then,find the eccentricity of the ellipse.(A) (1)/(2) (B) (sqrt(3))/(2) (C) (1)/(sqrt(2))(D)(1)/(sqrt(3))

P is a point on the ellipse x^2/(25)+y^2/(9) and Q is corresponding point of P on its auxiliary circle. Then the locus of point of intersection of normals at P" & "Q to the respective curves is