Find the equation of the normal to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` at the positive end of the latus rectum.

Find the length of Latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 .

Find the equation of tangent nad normal to the ellipse 4x^(2)+y^(2)=32 at theta=(pi)/(4) .

Find the normal to the ellipse (x^2)/(18)+(y^2)/8=1 at point (3, 2).

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 (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

Find the equations of tangent and normal to the ellipse x^(2)+4y^(2)=32 when theta=(pi)/(4) .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

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 ___

Find the equation of the normal to the circle x^(2)+y^(2)=9 at the point (1//sqrt(2), 1// sqrt(2)) .

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)