Precalculus : Identify the Conic With a Given Polar Equation

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Identify The Conic With A Given Polar Equation

Given the polar equation, determine the conic section:

Possible Answers:

Parabola

Hyperbola

Ellipse

Correct answer:

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 #2 : Identify The Conic With A Given Polar Equation

Given the polar equation, determine the conic section:

Possible Answers:

Hyperbola

Ellipse

Parabola

Correct answer:

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 #3 : Identify The Conic With A Given Polar Equation

Given the polar equation, determine the conic sectioN:

Possible Answers:

Hyperbola

Parabola

Ellipse

Correct answer:

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 #1432 : Pre Calculus

Given the polar equation, determine the conic section:

Possible Answers:

Parabola

Ellipse

Hyperbola

Correct answer:

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 #1433 : Pre Calculus

Given the polar equation, determine the conic section:

Possible Answers:

Ellipse

Parabola

Hyperbola

Correct answer:

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 #6 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Possible Answers:

Ellipse

Hyperbola

Parabola

Correct answer:

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 #1434 : Pre Calculus

Given the polar equation, identify the conic section:

Possible Answers:

Parabola

Hyperbola

Ellipse

Correct answer:

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 #1435 : Pre Calculus

Given the polar equation, identify the conic section:

Possible Answers:

Ellipse

Parabola

Hyperbola

Correct answer:

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 #9 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Possible Answers:

Hyperbola

Parabola

Ellipse

Correct answer:

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 #10 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Possible Answers:

Parabola

Ellipse

Hyperbola

Correct answer:

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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