# Precalculus : Polar Equations of Conic Sections

## Example Questions

### Example Question #1 : 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.

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:

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.

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:

Hyperbola

Parabola

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 #4 : Identify The Conic With A Given Polar Equation

Given the polar equation, determine the conic section:

Hyperbola

Ellipse

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.

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

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 #1 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Parabola

Ellipse

Hyperbola

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 #21 : Conic Sections

Given the polar equation, identify the conic section:

Ellipse

Parabola

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 #8 : Polar Equations Of Conic Sections

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 #9 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Hyperbola

Parabola

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 #1 : Polar Equations Of Conic Sections

Given the polar equation, identify the conic section.

Hyperbola

Ellipse

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.