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

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

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Answer 1 · 2018-04-09T15:41:02

See below.

Explanation:

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

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

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Identify an axis of revolution and generating conic of the surface 4x2+25y2+4z2=1004x^2+25y^2+4z^2=100. does this conic also generate x225+y24+z225=1x^2/25+y^2/4+z^2/25=1?

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