8. Conic Sections

Determine the vertices and foci of the following ellipse: $\(\frac{x^2}{49}\)+\(\frac{y^2}{36}\)=1$.

Graph the ellipse $\frac{{(x-1)}^2}{9}+\frac{{(y+3)}^2}{4}=1$.

Determine the vertices and foci of the ellipse $\(\left\)(x+1\(\right\))^2+\(\frac{\left(y-2\right)^2}{4}\)=1$.

Find the standard form of the equation for an ellipse with the following conditions.

Foci = $\(\left\)(-5,0\(\right\)),\(\left\)(5,0\(\right\))$

Vertices = $\(\left\)(-8,0\(\right\)),\(\left\)(8,0\(\right\))$

Given the ellipse equation $\(\frac{x^2}{16}\)+\(\frac{y^2}{4}\)=1$, determine the magnitude of the semi-major axis (a) and the semi-minor axis (b).

Given the equation $\(\frac{x^2}{4}\)+\(\frac{y^2}{9}\)=1$, sketch a graph of the ellipse.

Determine the vertices and foci of the following ellipse: $\(\frac{x^2}{9}\)+\(\frac{y^2}{16}\)=1$.