Question

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 asymptotes9x^{2} - 4y^{2} + 54x + 32y + 119 = 0

Conic sections

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 $$9x^{2}\ -\ 4y^{2}\ +\ 54x\ +\ 32y\ +\ 119 = 0$$

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