8. Conic Sections

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

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).

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

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

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

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

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

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

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

Graph the ellipse and locate the foci. (y^2)/25 + (x^2)/16 = 1

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (-4,0), (4,0); Vertices: (-5,0) (5,0)

Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis horizontal with length 12; length of minor axis = 4; center: (-3,5)

Graph the ellipse and locate the foci. 9x^2 + 4y^2 - 18x + 8y -23 = 0

In Exercises 1–18, graph each ellipse and locate the foci. x²/16+y²/4 = 1

Graph the ellipse and locate the foci. $\frac{x^2}{36}+\frac{y^2}{25}=1$

In Exercises 1–18, graph each ellipse and locate the foci. x²/9 +y²/36= 1

In Exercises 1–18, graph each ellipse and locate the foci. x²/25 +y²/64 = 1