Find the equation of the graph for each conic in standard form. Identify the conic, the center, the co-vertex, the focus (foci), major axis, minor axis, a^{2}, b^{2}, and c^{2}. For hyperbola, find the asymptotes 9x^{2} - 4y^{2} + 54x + 32y + 119 = 0

Question
Conic sections
asked 2021-01-25
Find the equation of the graph for each conic in standard form. Identify the conic, the center, the co-vertex, the focus (foci), major axis, minor axis, \(a^{2}, b^{2},\ and c^{2}.\) For hyperbola, find the asymptotes \(9x^{2}\ -\ 4y^{2}\ +\ 54x\ +\ 32y\ +\ 119 = 0\)

Answers (1)

2021-01-26
Consider the equation \(9(x^{2}\ \mp\ 6x\ +\ 1)\ -\ 9x\ \times\ 4(y^{2}\ -\ 4y\ +\ 4)\ +\ 32y=119\)
\(foci\ = (h\ \pm\ ae,\ k)\)
\((1, \pm\ 5,\ 2)\)
\((6,\ 2)\ (−4,\ 2)\)
\(vertices\ = (h\ \pm\ a,\ k)\ (h\ \pm\ k,\ b)\)
\((1\ \pm\ 4,\ 2)\ (1\ \sqrt{2\ \pm,\ 3})\)
\((5,\ 2)(−3,\ 2)\ (1,\ 1)(1,\ −5)\)
\(\frac{major\ axis}{minor\ axis}=8\ +\ 6\)
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