DeepConic sections

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.5 Parabolas, Ellipses, and Hyperbolas, #39 · Geometry · Conic sections

… is part of … and … is part of

This problem is about parabolas, are about ellipses, are about hyperbolas.

$y^{2} - 4 y$ is part of $(y - 2)^{2} =______$ and $2 x^{2} + 12 x$ is part of $2 (x + 3)^{2} =______$ . Therefore $y^{2} - 4 y - 2 x^{2} - 12 x = 0$ gives the hyperbola $(y - 2)^{2} - 2 (x + 3)^{2} =______$ . Its center is \_\_\_\_\_\_ and it opens to the \_\_\_\_\_\_.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.5 Parabolas, Ellipses, and Hyperbolas, #39

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