Let the equations of two ellipses be `E_1=x^2/3+y^2/2=1 and x^2/16+y^2/b^2=1`.If the product of their eccentricities is `1/2`, then the length of the minor axis of ellipse `E_2` is

Consider the ellipses E_1:x^2/9+y^2/5=1 and E_2: x^2/5+y^2/9=1 . Both the ellipses have

E_1:x^2/81 +y^2/b^2=1 and E_2: x^2/b^2+y^2/49=1 two ellipses having the same eccentricity if b^2 is equal to

Let the equation of ellipse be x^(2)/(a^(2)+1)=y^(2)/(a^(2)+2)=1 Statement 1 If eccentricity of the ellipse be 1/sqrt6 , then length of latusrectum is 10/sqrt6 . Statement 2 Length of latusrectum= (2(a^(2)+1))/(sqrt(a^(2)+2))

The given equation of the ellipse is (x^(2))/(81) + (y^(2))/(16) =1 . Find the length of the major and minor axes. Eccentricity and length of the latus rectum.

If the eccentricity of the ellipse x^2/25+y^2/a^2=1 and x^2/a^2+y^2/16=1 is same, then the value of a^2 is :

If x^2/(sec^2 theta) +y^2/(tan^2 theta)=1 represents an ellipse with eccentricity e and length of the major axis l then

The ellipse x^2/a^2+y^2/b^2=1,(a gt b) passes through (2,3) and have eccentricity equal to 1/2 . Then find the equation of normal to the ellipse at (2,3) .

Let e_(1) be the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 and e_(2) be the eccentricity of the ellipse x^(2)/a^2+(y^(2))/(b^(2))=1,a>b ,which passes through the foci of the hyperbola.If e_(1)e_(2)=1 ,then the length of the chord of the ellipse parallel to the "x" -axis and passing through (0,2) is :

Find the equation of the ellipse whose eccentricity is 1/2 , a focus is (2,3) and a directrix is x=7. Find the length of the major and minor axes of the ellipse .