# Precalculus : Identify the Conic With a Given Polar Equation

## Example Questions

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### Example Question #17 : Conic Sections

Given the polar equation, determine 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.

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

### Example Question #18 : Conic Sections

Given the polar equation, determine the conic section:

Ellipse

Parabola

Hyperbola

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 : Identify The Conic With A Given Polar Equation

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 #2 : Identify The Conic With A Given Polar Equation

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 #3 : Identify The Conic With A Given Polar Equation

Given the polar equation, determine 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 #4 : Identify The Conic With A Given Polar Equation

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.

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

### Example Question #5 : Identify The Conic With A Given Polar Equation

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 #6 : Identify The Conic With A Given Polar Equation

Given the polar equation, identify 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 #7 : Identify The Conic With A Given Polar Equation

Given the polar equation, identify 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.

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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