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Graphing Conic Sections

Graph the ellipse with the equation: $\frac{(y+1)^2}{64} + \frac{(x-5)^2}{28}=1$

64>28 so 64 = $a^2$

$\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}=1$

Center: (h,k)

Vertices: (h,k $\pm$ a)

Covertices: (h $\pm$ b,k)

$a^2 =64 b^2 -28$

$\sqrt{a^2}=\sqrt{64}$ $\sqrt{b^2}=\sqrt{28}$

a=8 b=5.29

Graph the hyperbola with the equation: $\frac{x^2}{64} - \frac{y^2}{49}$ =1

Length of traverse axis=2a vertices are endpoints of traverse axis

center, (0,0) $l_T = 2a$ 64= $a^2$ 8=a

$l_T=(2)(8)=16$

Endpoints: (-8,0)(8,0)