Find the eccentricity of the ellipse `x^(2)/(a^(2))+y^(2)/b^(2)=1` when a=5 and b=3.

Find the eccentricity of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 whose latus rectum is half of its major axis.

The eccentricity of the ellipse 4x^2 + 9y^2 = 36 is :

Find the area of enclosed by the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 .

If a=[t^(2)-3t+4] and b=[3+5t] , where [.] donates the greatest integer function, then the latusrectum of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 at t=3/2 is

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

Find the locus of the points of the intersection of tangents to ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 which make an angle theta.

Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=1 whose distance from the center of the ellipse is sqrt(5)

If the eccentricities of the two ellipse (x^(2))/(169)+(y^(2))/(25)=1 and (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and equal , then the value (a)/(b) , is