Recent questions in Conic sections

Conic sections

asked 2021-03-11

A solid is formed by cutting a conical section away a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?

Conic sections

asked 2021-03-09

The eccentricities of conic sections with one focus at the origin and the directrix corresponding and sketch a graph:
\(\displaystyle{e}={2},\)
\(directrix \displaystyle{r}=-{2} \sec{\theta}.\)

Conic sections

asked 2021-03-07

Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. \(\displaystyle{r}=\ {\frac{{{10}}}{{{5}\ +\ {2}\ {\cos{\theta}}}}}\)

Conic sections

asked 2021-03-07

To calculate the verties and foci of the conic section: \(\displaystyle{\left({x}{9}\right)}{2}\ +\ {\left({y}{4}\right)}{2}={1}\)

Conic sections

asked 2021-03-07

To calculate: The sections represented by the polar equation \(\displaystyle{r}=\frac{18}{{{6}-{6} \cos{\theta}}}\) and graph it by the use of graphing utility.

Conic sections

asked 2021-03-06

If the directrix is horizontal, then the parabola opens \((\text{horizontally}/\text{vertically})\)

Conic sections

asked 2021-03-05

A latus rectum of a conic section is a chord through a focus parallel to the directrix. Find the area bounded by the parabola \(\displaystyle{y}={x}^{2}\text{/}{\left({4}{c}\right)}\) and its latus rectum.

Conic sections

asked 2021-02-25

Find the required information and graph:
\(\displaystyle{2}{x}^{2}+{2}{y}^{2}+{2}{x}+{14}{y}+{17}={0}\)

Conic sections

asked 2021-02-25

Identify the equation without applying a rotation of axes.
\(\displaystyle{4}{x}^{2}-{8}{x}{y}+{4}{y}^{2}-{3}{x}+{6}={0}\)

Conic sections

asked 2021-02-22

Identify the type of conic section whose equation is given.
Given:
\(\displaystyle{2}{x}^{2}={y}^{2}+{2}\)
To determine: The type of conics.

Conic sections

asked 2021-02-22

Given the following conic section, determine its shape and then sketch its graph.
\(\displaystyle{x}^{2}-{2}{x}{y}+{y}^{2}+{x}-{2}{y}-{1}={0}\)

Conic sections

asked 2021-02-20

To find the vertices and foci of the conic section: \(\displaystyle{\frac{{{\left({x}\ -\ {4}\right)}^{{{2}}}}}{{{5}^{{{2}}}}}}\ -\ {\frac{{{\left({y}\ +\ {3}\right)}^{{{2}}}}}{{{6}^{{{2}}}}}}={1}\)

Conic sections

asked 2021-02-15

Determine whether the statement If \(\displaystyle{D}\ne{0}{\quad\text{or}\quad}{E}\ne{0}\),
then the graph of \(\displaystyle{y}^{2}-{x}^{2}+{D}{x}+{E}{y}={0}\) is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

Conic sections

asked 2021-02-14

A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.

Conic sections

asked 2021-02-12

Identify the conic section given by the polar equation \(\displaystyle{r}=\frac{4}{{{1}- \cos{\theta}}}\) and also determine its directrix.

Conic sections

asked 2021-02-11

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

Conic sections

asked 2021-02-10

Identify the conic section given by \(\displaystyle{y}^{2}+{2}{y}={4}{x}^{2}+{3}\)
Find its \(\frac{\text{vertex}}{\text{vertices}}\ \text{and}\ \frac{\text{focus}}{\text{foci}}\)

Conic sections

asked 2021-02-05

Determine the equation of a conic section...(Hyperbola) Given: center (-9, 1) distance between \(\displaystyle{F}{1}{\quad\text{and}\quad}{F}{2}={20}\) units
distance between \(\displaystyle{C}{V}{1}{\quad\text{and}\quad}{C}{V}{2}={4}\) units orientation = vertical

Conic sections

asked 2021-01-31

To calculate: The vertices and foci of the conic section: \(\displaystyle{x}{29}\ +\ {y}{24}={1}\)

Conic sections

asked 2021-01-31

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Recent questions in Conic sections

A solid is formed by cutting a conical section away a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?

The eccentricities of conic sections with one focus at the origin and the directrix corresponding and sketch a graph:
\(\displaystyle{e}={2},\)
\(directrix \displaystyle{r}=-{2} \sec{\theta}.\)

Polar equations for conic sections Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. \(\displaystyle{r}=\ {\frac{{{10}}}{{{5}\ +\ {2}\ {\cos{\theta}}}}}\)

To calculate the verties and foci of the conic section: \(\displaystyle{\left({x}{9}\right)}{2}\ +\ {\left({y}{4}\right)}{2}={1}\)

To calculate: The sections represented by the polar equation \(\displaystyle{r}=\frac{18}{{{6}-{6} \cos{\theta}}}\) and graph it by the use of graphing utility.

If the directrix is horizontal, then the parabola opens \((\text{horizontally}/\text{vertically})\)

A latus rectum of a conic section is a chord through a focus parallel to the directrix. Find the area bounded by the parabola \(\displaystyle{y}={x}^{2}\text{/}{\left({4}{c}\right)}\) and its latus rectum.

Find the required information and graph:
\(\displaystyle{2}{x}^{2}+{2}{y}^{2}+{2}{x}+{14}{y}+{17}={0}\)

Identify the equation without applying a rotation of axes.
\(\displaystyle{4}{x}^{2}-{8}{x}{y}+{4}{y}^{2}-{3}{x}+{6}={0}\)

Identify the type of conic section whose equation is given.
Given:
\(\displaystyle{2}{x}^{2}={y}^{2}+{2}\)
To determine: The type of conics.

Given the following conic section, determine its shape and then sketch its graph.
\(\displaystyle{x}^{2}-{2}{x}{y}+{y}^{2}+{x}-{2}{y}-{1}={0}\)

To find the vertices and foci of the conic section: \(\displaystyle{\frac{{{\left({x}\ -\ {4}\right)}^{{{2}}}}}{{{5}^{{{2}}}}}}\ -\ {\frac{{{\left({y}\ +\ {3}\right)}^{{{2}}}}}{{{6}^{{{2}}}}}}={1}\)

Determine whether the statement If \(\displaystyle{D}\ne{0}{\quad\text{or}\quad}{E}\ne{0}\),
then the graph of \(\displaystyle{y}^{2}-{x}^{2}+{D}{x}+{E}{y}={0}\) is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.

Identify the conic section given by the polar equation \(\displaystyle{r}=\frac{4}{{{1}- \cos{\theta}}}\) and also determine its directrix.

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

Identify the conic section given by \(\displaystyle{y}^{2}+{2}{y}={4}{x}^{2}+{3}\)
Find its \(\frac{\text{vertex}}{\text{vertices}}\ \text{and}\ \frac{\text{focus}}{\text{foci}}\)

Determine the equation of a conic section...(Hyperbola) Given: center (-9, 1) distance between \(\displaystyle{F}{1}{\quad\text{and}\quad}{F}{2}={20}\) units
distance between \(\displaystyle{C}{V}{1}{\quad\text{and}\quad}{C}{V}{2}={4}\) units orientation = vertical

To calculate: The vertices and foci of the conic section: \(\displaystyle{x}{29}\ +\ {y}{24}={1}\)

Convert the following equations to its standard form and identify the vertex and focus.
\(\displaystyle{3}{y}^{2}+{8}{x}+{24}{y}+{40}={0}\)

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Recent questions in Conic sections