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 an angle `beta` with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by `e=cosbeta/(cosalpha)`

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 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

The equation of tangent to the ellipse 2x^(2)+3y^(2)=6 which make an angle 30^(@) with the major axis is

The equation of tangent to the ellipse 2x^(2)+3y^(2)=6 which make an angle 30^(@) with the major axis is

The tangents drawn from a point P to ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 make angles alpha and beta with the transverse axis of the hyperbola, then

The tangent at the point theta on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , meets its auxiliary circle at two points whose join subtends a right angle at the centre, show that the eccentricity of the ellipse is given by, (1)/(e^(2))=1+sin^(2)theta

If the tangents to ellipse x^2/a^2 + y^2/b^2 = 1 makes angle alpha and beta with major axis such that tan alpha + tan beta = lambda then locus of their point of intersection is

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.