Find the length of the minor axis of the ellipse generated when the surface $z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }$ is intersected by the plane $z = 5$
A) 25
B) $10 \sqrt { 10 }$
C) $5 \sqrt { 5 }$
D) 5
E) 10

Question

Quizplus · Accepted Answer

The intersection of the plane $z = 5$ with the surface $z = \frac{x^2}{5} + \frac{y^2}{25}$ gives the equation $\frac{x^2}{5} + \frac{y^2}{25} = 5$. This can be rewritten as $\frac{x^2}{25} + \frac{y^2}{125} = 1$, which is the equation of an ellipse with semi-major axis $\sqrt{125} = 5\sqrt{5}$ and semi-minor axis $\sqrt{25} = 5$. The length of the minor axis is $2 \times 5 = 10$.

Find the Length of the Minor Axis of the Ellipse z=x25+y225z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }z=5x2​+25y2​

Find the Length of the Minor Axis of the Ellipse $z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }$