Home > Student Resources > Graphing Conic Sections Given Equations

Graphing Conic Sections Given Equations

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 ± a)

covertices: (h ± b, k)

$a^{2}=64$ → $\sqrt{a^2}=\sqrt{64}$ → $a=8$

$b^{2}=28$ → $\sqrt{b^2}=\sqrt{28}$ → $a=5.29$

vertices:

covertices:

Center: (5, -1)

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

64 > 49 so 64 = $a^e$

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

length of tranverse axis = 2a

vertices are endpoints of transverse axis

center, (0, 0)

$l_{t}=2a, 64=a^{2}. 8=a$

$l_{t}=(2)(8)=16\_ endpoints: (-8, 0), (8, 0) asymptotes: \(y=\frac{b}{a}x, b^{2}=4a$

$y=\frac{7}{8}x, b=7$