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

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

Question
Conic sections
asked 2021-02-05
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 \(16x^2 + 64x - 9y^2 + 18y - 89 = 0\)

Answers (1)

2021-02-06
Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered. a) Since the coefficients of \(x^2 and y^2\) are of opposite signs. 16 and -9. So it is an equation of hyperbola. Answer(a): Hyperbola b) To find the standard form of the equation we have to complete squares for x and y portions separately. Add 89 to both sides \(16x^2 + 64x - 9y^2 + 18y - 89 = 0\)
\(16x^2 + 64x - 9y^2 + 18y = 89\) Factor out 16 from the x portion and -9 from the y portion \(16(x^2 + 4x) - 9(y^2 - 2y) = 89\) Then complete square for each section and to balance right side add or subtract the same amount. \(16(x^2 + 4x + 4) - 9(y^2 - 2y + 1) = 89 + 16 (4) - 9(1)\)
\(16(x + 2)^2 - 9(y - 1)^2 = 144\) Then divide both sides by 144 \(\frac{16(x + 2)^2}{144} - \frac{9(y - 1)^2}{144} = \frac{144}{144}\)
\(\frac{(x+2)^2}{9} - \frac{(y - 1)^2}{16} = 1\) Answer \(\frac{(x+2)^2}{9} - \frac{(y - 1)^2}{16} = 1\)
0

Relevant Questions

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 \(9x^{2}\ -\ 4y^{2}\ +\ 54x\ +\ 32y\ +\ 119 = 0\)
asked 2020-12-24
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. \(x2\+\ y2\ −\ 4x\ −\ 6y\ +\ 1 = 0\)
asked 2020-11-12
Find and calculate the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections \(x^2 + 2y^2 - 2x - 4y = -1\)
asked 2021-01-06
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)
asked 2021-01-31
Find the center, foci, vertices, asymptotes, and radius, if necessary, of the conic sections in the equation:
\(\displaystyle{x}^{2}+{4}{x}+{y}^{2}={12}\)
asked 2020-12-27
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
asked 2021-05-17
Find an equation of the conic described.graph the equation. Parabola:focus(-1,4.5) vertex (-1,3).
asked 2021-02-10
Identify the conic section given by \(\displaystyle{y}^{2}+{2}{y}={4}{x}^{2}+{3}\)
Find its \(\frac{\text{vertex}}{\text{vertices}}\ \text{and}\ \frac{\text{focus}}{\text{foci}}\)
asked 2021-02-25
Give the eccentricities of conic sections with one focus at the origin along with the directrix corresponding to that focus. Find a polar equation for each conic section. \(e = 2,\ x = 4\)
asked 2020-11-09
Identify the conic with th e given equa­tion and give its equation in standard form \(6x^2 - 4xy + 9y^2 - 20x - 10y - 5 = 0\)
...