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

### Relevant Questions

For Exercise, a. Identify the equation as representing a circle, an ellipse, a hyperbola, or a parabola. b. Graph the curve. c. Identify key features of the graph. That is. If the equation represents a circle, identify the center and radius. • If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity. • If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity. • If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the directrix, and equation of the axis of symmetry. $$x2\+\ y2\ −\ 4x\ −\ 6y\ +\ 1 = 0$$
Write the equation of each conic section, given the following characteristics:
a) Write the equation of an ellipse with center at (3, 2) and horizontal major axis with length 8. The minor axis is 6 units long.
b) Write the equation of a hyperbola with vertices at (3, 3) and (-3,3). The foci are located at (4, 3) and (-4, 3).
c) Write the equation of a parabola with vertex at (-2,4) and focus at (-4, 4)
Write the equation of each conic section, given the following characteristics:
a) Write the equation of an ellipse with center at (3, 2) and horizontal major axis with length 8. The minor axis is 6 units long.
b) Write the equation of a hyperbola with vertices at (3, 3) and (-3, 3). The foci are located at (4, 3) and (-4, 3).
c) Write the equation of a parabola with vertex at (-2, 4) and focus at (-4, 4)
a) determine the type of conic b) find the standard form of the equation Parabolas: vertex, focus, directrix Circles: Center, radius Ellipses: center, vertices, co-vertices, foci Hyperbolas: center, vertices, co-vertices, foci, asymptotes $$16x^2 + 64x - 9y^2 + 18y - 89 = 0$$
Instructions: Graph the conic section and make sure to label the coordinates in the graph. Include all the calculations needed to complete the graph. Give the standard form (SF) and the general form (GF) of the conic sections. HYPERBOLA: 1) The vertices are at (-2, 0) and (2, 0). The conjugate axis' length is 6.
Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections $$x^2 + 2y^2 - 2x - 4y = -1$$
3. The hyperbola given by $$\displaystyle{5}{x}^{2}-{4}{y}^{2}={20}{x}+{24}{y}+{36}.$$
Solve, a. If necessary, write the equation in one of the standard forms for a conic in polar coordinates $$r = \frac{6}{2 + sin \theta}$$ b. Determine values for e and p. Use the value of e to identify the conic section. c. Graph the given polar equation.
Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $$x = h + r cos(?), y = k + r sin(?)$$ Use your result to find a set of parametric equations for the line or conic section. $$(When 0 \leq ? \leq 2?.)$$ Circle: center: (6, 3), radius: 7
$$\displaystyle{x}^{2}+{4}{x}+{y}^{2}={12}$$