Precalculus : Identify the Conic With a Given Polar Equation

Example Questions

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Example Question #11 : Conic Sections

Given the polar equation, determine the conic section: Ellipse

Hyperbola

Parabola

Hyperbola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

Now, for the given conic section, so it must be a hyperbola.

Example Question #12 : Conic Sections

Given the polar equation, determine the conic section: Ellipse

Hyperbola

Parabola

Ellipse

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

Now, for the given conic section, so it must be an ellipse.

Example Question #1 : Polar Equations Of Conic Sections

Given the polar equation, determine the conic sectioN: Parabola

Hyperbola

Ellipse

Ellipse

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be an ellipse.

Example Question #22 : Conic Sections

Given the polar equation, determine the conic section: Hyperbola

Parabola

Ellipse

Parabola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be a parabola.

Example Question #1 : Polar Equations Of Conic Sections

Given the polar equation, determine the conic section: Parabola

Ellipse

Hyperbola

Hyperbola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be a hyperbola.

Example Question #24 : Conic Sections

Given the polar equation, identify the conic section. Parabola

Hyperbola

Ellipse

Parabola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

Now, for the given conic section, so it must be a parabola.

Example Question #25 : Conic Sections

Given the polar equation, identify the conic section: Parabola

Hyperbola

Ellipse

Hyperbola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be a hyperbola.

Example Question #26 : Conic Sections

Given the polar equation, identify the conic section: Hyperbola

Ellipse

Parabola

Hyperbola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be a hyperbola.

Example Question #27 : Conic Sections

Given the polar equation, identify the conic section. Hyperbola

Ellipse

Parabola

Ellipse

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be an ellipse.

Example Question #28 : Conic Sections

Given the polar equation, identify the conic section. Ellipse

Hyperbola

Parabola

Parabola

Explanation:

Recall that the polar equations of conic sections can come in the following forms:  , where is the eccentricity of the conic section.

To determine what conic section the polar graph depicts, look only at the conic section's eccentricity. will give an ellipse. will give a parabola. will give a hyperbola.

First, put the given polar equation into one of the forms seen above by dividing everything by . Now, for the given conic section, so it must be a parabola.

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