Given positive numbers [math]a,b,c[/math] an [b]ellipsoid[/b] is given by the equation[br][center][br][math]\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1.[/math][/center]
Change [math]a[/math] from [math]1[/math] to [math]3[/math]. What happens to the object?
The object gets stretched by a factor of [math]3[/math] parallel to the [math]x[/math]-axis.
Change [math]b[/math] from [math]1[/math] to [math]2[/math]. What happens to the object?
The object gets stretched by a factor of [math]2[/math] parallel to the [math]y[/math]-axis.
Change [math]b[/math] from [math]2[/math] to [math]1.5[/math]. What happens to the object?
The object gets stretched by a factor of [math]\frac{3}{4}[/math] parallel to the [math]y[/math]-axis.
Change [math]c[/math] from [math]1[/math] to [math]3[/math]. What happens to the object?
The object gets stretched by a factor of [math]3[/math] parallel to the [math]z[/math]-axis.