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 equation of the normal to the hyperbola x^(2)-3y^(2)=144 at the positive end of the latus rectum.

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

Find the equations of tangent and normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at (x_1,y_1)

Find the equations of the tangent and normal to the parabola y^(2) =6x at the positive end of the latus rectum

Find the equation of tangent and normal to the ellipse x^2+8y^2=33 at (-1,2).

Find the length of latus rectum of the ellipse (x^(2))/(25) + (y^(2))/(36) = 1 .

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

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.

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 monor 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 ___