[LEFT]Determine the length of the ray focal of the point $\displaystyle M(3,\frac{7}{4}) $who is on the ellipse $\displaystyle 7x^2+16y^2=112$
Answer:
$\displaystyle \frac{25}{4}$ and $\displaystyle \frac{7}{4}$
That ellipse can also be written (divide both sides by 112) $\displaystyle \frac{x^2}{112}+ \frac{y^2}{7}= \frac{x^2}{(4\sqrt{7})^2}+ \frac{y^2}{(\sqrt{7})^2}= 1$.
That has semi-axes of length $\displaystyle \sqrt{7}$ and $\displaystyle 4\sqrt{7}$. Can you calculate the coordinates of the foci from that? Then it should be easy to find the distance from that point to each point.