let-an-ellipse-be-defined-by-x2m2y2n21-fracx2m2-fracy2n2-1-for-a-point-xy-x-y-on

Question

Let an ellipse be defined by x2m2+y2n2=1 \frac{$$x^2$$}{$$m^2$$} + \frac{$$y^2$$}{$$n^2$$} = 1 . For a point (x,y) (x, y)  on the ellipse, let s2 $$s^2  be $$the square of its distance to the center. Find the average value of s2 $$s^2  as x x  $$runs from −m -m   to m m .

Accepted Answer

m2+2n23\frac{$$m^2$$ + $$2n^2$$}{3}

Answer

2m2+n23\frac{$$2m^2$+n^2$$}{3}

Answer

3m2+2n23\frac{$$3m^2$+2n^2$$}{3}

Answer

m2−2n23\frac{$$m^2$-2n^2$$}{3}

Let an ellipse be defined by x2m2+y2n2=1 \(\frac{x^2}{m^2}\) + \(\frac{y^2}{n^2}\) = 1 . For a point (x,y) (x, y) on the ellipse, let s2 s^2 be the square of its distance to the center. Find the average value of s2 s^2 as x x runs from −m -m to m m .

Let an ellipse be defined by $\frac{x^{2}}{m^{2}} + \frac{y^{2}}{n^{2}} = 1$ . For a point $(x, y)$ on the ellipse, let $s^{2}$ be the square of its distance to the center. Find the average value of $s^{2}$ as $x$ runs from $- m$ to $m$ .