If the ellipse `with equation 9x^2 + 25y^2 = 225` find ecentricity & foci

If the ellipse with equation 9x^2+25y^2=225 , then find the eccentricity and foci.

Given the ellipse with equation x^(2) + 4y^(2) = 16 , find the length of major and minor axes, eccentricity, foci and vertices.

(i) Find the equation of hyperbola whose eccentricity is sqrt((13)/(12)) and the distance between foci is 26. (ii) The foci of a hyperbola coincide of the ellipse 9x^(2)+25y^(2)=225 . If the eccentricity of the hyperbola is 2, then find its equation.

If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1 , then find the ecentricity angle theta of point of contact.

Find the length of the major axis of the ellipse whose focus is (-1,1) directrix is x-y+3=0 and ecentricity is 1/2 .

The foci of a hyperbola coincide with the foci of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 . If the eccentricity of the hyperbola is 2 , then the equation of the tangent of this hyperbola passing through the point (4,6) is

If e_1 is the eccentricity of the ellipse x^2/16+y^2/25=1 and e_2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e_1 e_2=1 , then equation of the hyperbola is

Show that x^2+4y^2-2x+16 y+13=0 is the equation of an ellipse. Find its eccentricity, vertices, foci, directices and , the length and the equation of the latus-rectum.

For the ellipse 9x^2 + 16y^2 = 144 , find the length of the major and minor axes, the eccentricity, the coordinatse of the foci, the vertices and the equations of the directrices.

Find the length and equation of major and minor axes, centre, eccentricity, foci, equation of directrices, vertices and length of latus rectum of the ellipses : x^2/225 + y^2/289 =1