# Get help with conic sections equations Recent questions in Conic sections
Conic sections
ANSWERED ### Convert the following equations to its standard form and identify the vertex and focus. $$\displaystyle{3}{y}^{2}+{8}{x}+{24}{y}+{40}={0}$$

Conic sections
ANSWERED ### Find the center, foci, vertices, asymptotes, and radius, if necessary, of the conic sections in the equation: $$\displaystyle{x}^{2}+{4}{x}+{y}^{2}={12}$$

Conic sections
ANSWERED ### The polar equation of the conic with the given eccentricity and directrix and focus at origin: $$\displaystyle{r}={41}\ +\ {\cos{\theta}}$$

Conic sections
ANSWERED ### The exercise provides the equation for a degenerate conical section. Fill in the square and describe the graph of each equation. $$\displaystyle{4}{x^2}-{y^2}-{32}{x}-{4}{y}+{60}={0}$$

Conic sections
ANSWERED ### To calculate: The equation $$100y^{2}\ +\ 4x=x^{2}\ +\ 104$$ in one of standard forms of the conic sections and identify the conic section.

Conic sections
ANSWERED ### Word problem involving comic sections. A hall 100 feet in length is designed as a whispering gallery (See example 9 for Ellipses). If the focus is 25 feet from the center, how high will the ceiling be at the center?

Conic sections
ANSWERED ### 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)

Conic sections
ANSWERED ### The type of the conic section using the Discriminant Test and plot the curve using a computer algebra system. $$\displaystyle{x}^{2}\ -\ {2}{x}{y}\ +\ {y}^{2}\ +\ {24}{x}\ -\ {8}={0}$$

Conic sections
ANSWERED ### The conclusion about the values of e for rlliptical equations. The provided equations of conic sections are, A) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{36}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{13}}}}={1}$$ B) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{4}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{4}}}}={1}$$ C) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{25}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{16}}}}={1}$$ D) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{25}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{39}}}}={1}$$ E) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{17}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{81}}}}={1}$$ F) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{36}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{36}}}}={1}$$ G) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{16}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{65}}}}={1}$$ H) $$\displaystyle{\frac{{{x}^{{{2}}}}}{{{144}}}}\ -\ {\frac{{{y}^{{{2}}}}}{{{140}}}}={1}$$

Conic sections
ANSWERED ### For Exercise, an equation of a degenerate conic section is given. Complete the square and describe the graph of each equation. $$\displaystyle{9}{x}{2}+{4}{y}{2}-{24}{y}+{36}={0}$$

Conic sections
ANSWERED ### To determine: The conic section and to find the vertices and foci: $$\displaystyle{x}^{2}\ -\ {y}^{2}{y}={4}$$

Conic sections
ANSWERED ### Use the Discriminant Test to determine the type of the conic section (in every case non degenerate equation). Plot the curve if you have a computer algebra system. $$\displaystyle{2}{x}^{2}-{8}{x}{y}+{3}{y}^{2}-{4}={0}$$

Conic sections
ANSWERED ### (a) Given the conic section $$\displaystyle{r}=\frac{5}{{{7}+{3} \cos{{\left(\theta\right)}}}}$$, find the x and y intercept(s) and the focus(foci). (b) Given the conic section $$\displaystyle{r}=\frac{5}{{{2}+{5} \sin{{\left(\theta\right)}}}}$$, find the x and y intercept(s) and the focus(foci).

Conic sections
ANSWERED ### Find out what kind of conic section the following quadratic form represents and transform it to principal axes. Express $$\displaystyle\vec{{x}}^{T}={\left[{x}_{{1}}{x}_{{2}}\right]}$$ in terms of the new coordinate vector $$\displaystyle\vec{{y}}^{T}={\left[{y}_{{1}}{y}_{{2}}\right]}$$ $$\displaystyle{{x}_{{1}}^{{2}}}-{12}{x}_{{1}}{x}_{{2}}+{{x}_{{2}}^{{2}}}={70}$$

Conic sections
ANSWERED ### We need to verify theorem 5 Focus-Directrix definition: $$\displaystyle{0}\ {<}\ {e}\ {<}\ {1}\ \text{and}\ {c}={d}{\left({e}\ -\ {2}\ -\ {1}\right)}$$

Conic sections
ANSWERED ### Decide if the equation defines an ellipse, a hyperbola, a parabola, or no conic section at all. $$\displaystyle{\left({a}\right)}{4}{x}{2}-{9}{y}{2}={12}{\left({b}\right)}-{4}{x}+{9}{y}{2}={0}$$ $$\displaystyle{\left({c}\right)}{4}{y}{2}+{9}{x}{2}={12}{\left({d}\right)}{4}{x}{3}+{9}{y}{3}={12}$$

Conic sections
ANSWERED ### To find: The equation of the given hyperbola. The foci of the hyperbola is $$\displaystyle{\left({0},\ \pm\ {5}\right)}{\quad\text{and}\quad} \text{ entricity is }{e} -{1.5}$$.

Conic sections
ANSWERED ### The equation is $$\displaystyle{16}{x}^{2}+{9}{y}^{2}-{98}{x}+{5}{y}+{224}={0}$$

Conic sections
ANSWERED ### The conic for the equation $$\displaystyle{\left({x}+{1}\right)}^{2}={4}{\left(-{1}\right)}{\left({y}-{2}\right)}$$ and also describe the translation of the from standard position.
ANSWERED 