Raheem Donnelly

Answered 2021-08-11
Author has **19853** answers

asked 2021-08-13

Find an equation of the conic described.Graph the equation.

Ellipse; center at (0,0); focus at (0,3); vertex at (0, 5)

Ellipse; center at (0,0); focus at (0,3); vertex at (0, 5)

asked 2021-08-10

Show that the graph of an equation of the form

\(\displaystyle{A}{x}^{{2}}+{C}{y}^{{2}}+{D}{x}+{E}{y}+{F}={0},{A}\ne{0},{C}\ne{0}\)

where A and C are of opposite sign,

(a) is a hyperbola if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}\ne{0}\)

(b) is two intersecting lines if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}={0}\)

\(\displaystyle{A}{x}^{{2}}+{C}{y}^{{2}}+{D}{x}+{E}{y}+{F}={0},{A}\ne{0},{C}\ne{0}\)

where A and C are of opposite sign,

(a) is a hyperbola if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}\ne{0}\)

(b) is two intersecting lines if \(\displaystyle{\frac{{{D}^{{2}}}}{{{4}{A}}}}+{\frac{{{E}^{{2}}}}{{{4}{C}}}}-{F}={0}\)

asked 2021-08-11

\(\displaystyle{S}_{{1}},{S}_{{2}}\) are two foci of the ellipse \(\displaystyle{x}^{{2}}+{2}{y}^{{2}}={2}\). P be any point on the ellipse The locus incentre of the triangle \(\displaystyle{P}{S}{S}_{{1}}\), is a conic where length of its latus rectum is

asked 2021-08-09

Use the information provided to write the general conic form equation of each ellipse.

\(\displaystyle{\frac{{{x}^{{2}}}}{{{36}}}}+{\frac{{{y}^{{2}}}}{{{81}}}}={1}\)

\(\displaystyle{\frac{{{x}^{{2}}}}{{{36}}}}+{\frac{{{y}^{{2}}}}{{{81}}}}={1}\)

asked 2020-11-24

\(\displaystyle{\left({a}\right)}{4}{x}^{2}-{9}{y}^{2}={12}{\left({b}\right)}-{4}{x}+{9}{y}^{2}={0}\)

\(\displaystyle{\left({c}\right)}{4}{y}^{2}+{9}{x}^{2}={12}{\left({d}\right)}{4}{x}^{3}+{9}{y}^{3}={12}\)

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. \(x^2\ +\ y^2\ −\ 4x\ −\ 6y\ +\ 1 = 0\)

asked 2021-08-08

Find the equations of the parabolas that share a vertex and a focus with the ellipse. Draw the conics. \(\displaystyle{25}{x}^{{2}}+{9}{y}^{{2}}={9}\)