# Identify an axis of revolution and generating conic of the surface 4x^2+25y^2+4z^2=100. does this conic also generate x^2/25+y^2/4+z^2/25=1?

$4 {x}^{2} + 25 {y}^{2} + 4 {z}^{2} = 100$ and
${x}^{2} / 25 + {y}^{2} / 4 + {z}^{2} / 25 = 1$ represent the same surface which is an ellipsoid of revolution. It can be generated easily by rotating around the $y$ axis the proper ellipse.