CPM Homework Help : A2C Problem 13-125

For each of the following equations, identify the curve, write the equation in graphing form, and list the following information: center, focus or foci, and asymptotes. Refer to the Math Notes boxes in Lessons 11.2.2, 11.2.4, and 11.2.6 for definitions.

$2x^{2} + y^{2} − 4x + 6y − 7 = 0$
Answer (a):
$\frac{(x-1)^2}{9}+\frac{(y+3)^2}{18}=1$
Center: $\left(1, − 3\right)$
Foci: $\left(1, 0\right)$ and $\left(1, −6\right)$

$3y^{2} − x^{2} + 12y = 0$
Hint (b):
$\frac{(y+2)^2}{4}-\frac{x^2}{12}=1$
Now find the center, foci and asymptotes.

$12x^{2} + 8y^{2} + 48x − 48y + 24 = 0$
Hint (c):
See parts (a) and (b).