If the eccentricities of the ellipses `x^2/alpha^2 +| y^2/beta^2=1` and `x^2/a^2+y^2/b^2=1` be same show that `a beta=b alpha`

The eccentricities of the ellipse x^(2)/alpha^(2)+y^(2)/beta^(2)=1,alphagtbeta and x^(2)/9+y^(2)/16=1 are equal. Which one of the following is correct?

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

Prove that the equation of the chord joining the points 'a'&'b' on the ellipse x^2/a^2+y^2/b^2=1 is x/a cos((alpha+beta)/2)+y/b sin((alpha+beta)/2)=cos((alpha-beta)/2)

If alpha and beta are eccentric angles of the ends of a focal chord of the ellipse x^2/a^2 + y^2/b^2 =1 , then tan alpha/2 .tan beta/2 is (A) (1-e)/(1+e) (B) (e+1)/(e-1) (C) (e-1)/(e+1) (D) none of these

If the tangent at any point of an ellipse x^2/a^2 + y^2/b^2 =1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact then show that the eccentricity ‘e’ of the ellipse is given by the absolute value of cos beta/cos alpha

IF alpha , beta are eccentric angles of end points of a focal chord of the ellipse x^(2)/a^(2) + y^(2)/b^(2) =1 then tan(alpha /2) tan (beta/2) is equal to

The length of the Latusrectum of the ellipse ((x-alpha)^(2))/(a^(2))+((y-beta)^(2))/(b^(2))=1 (a

If the tangent at any point of the ellipse (x^(2))/(a^(3))+(y^(2))/(b^(2))=1 makes an angle alpha with the major axis and angle beta with the focal radius of the point of contact,then show that the eccentricity of the ellipse is given by e=cos(beta)/(cos alpha)

If the curves : alpha x^(2)+betay^(2)=1 and alpha'x^(2)+beta'y^(2)=1 intersect orthogonally, prove that (alpha-alpha')beta beta'=(beta-beta')alpha alpha' .