Question

Identify an axis of revolution and generating conic of the surface 4x^2+25y^2+4z^2=100. Does this conic also generate x^2/4 + y^2/25 + z^2/4=1?Give reasons for your answer.

Answer 1

Answer on Question #78891 – Math – Analytic Geometry Question

Identify an axis of revolution and generating conic of the surface

$4x^{2} + 25y^{2} + 4z^{2} = 100$. Does this conic also generate

$$\frac {x ^ {2}}{4} + \frac {y ^ {2}}{25} + \frac {z ^ {2}}{4} = 1$$

Give reasons for your answer.

Solution

$$\begin{array}{l} 4 x ^ {2} + 25 y ^ {2} + 4 z ^ {2} = 100 \\ \frac {4 x ^ {2} + 25 y ^ {2} + 4 z ^ {2}}{100} = \frac {100}{100} \\ \frac {x ^ {2} + z ^ {2}}{25} + \frac {y ^ {2}}{4} = 1 \\ \end{array}$$

We have the spheroid (ellipsoid of revolution). Its rotation axis is $y$-axis.

$$\frac {x ^ {2}}{4} + \frac {y ^ {2}}{25} + \frac {z ^ {2}}{4} = 1$$

We have the spheroid (ellipsoid of revolution). Its rotation axis is $y$-axis.

We see that both have the same rotation axis which is the $y$-axis.

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