Polar Equations and Conic Sections

Find the area enclosed by the polar curve

 $r=4\sin\theta$  and the limits  $\theta=0$  and  $\theta=\frac{\pi}{5}$  

• 0.411

• 0.511

• 0.611

• 0.711

• 0.811

What is the correct label for A?

• Focus

• Vertex

• Directrix

• Focal Axis

What is the correct label for D?

• Focus

• Vertex

• Directrix

• Focal Axis

The eccentricity of a conic section is denoted by the letter e. What type of conic section has e=1?

• Parabola

• Ellipse

• Hyperbola

• None of the above

The eccentricity of a conic section is denoted by the letter e. What type of conic section has e<1?

• Parabola

• Ellipse

• Hyperbola

• None of the above

The eccentricity of a conic section is denoted by the letter e. What type of conic section has e>1?

• Parabola

• Ellipse

• Hyperbola

• None of the above

Select the correct polar equation for a conic with  $e=\frac{2}{5}$  and a directrix at  $x=2$  

•  $r=\frac{4}{1+2\cos\theta}$  

•  $r=\frac{4}{5+10\cos\theta}$  

•  $r=\frac{4}{5+2\cos\theta}$  

•  $r=\frac{2}{5+2\cos\theta}$  

 Find a polar equation for a parabola that has a directrix at    $y=-3$  

•  $r=\frac{3}{1-\sin\theta}$  

•  $r=-\frac{3}{1-\sin\theta}$  

•  $r=\frac{3}{1+\sin\theta}$  

•  $r=-\frac{3}{1+\sin\theta}$  

If a conic section has an equation   $r=\frac{7}{5+3\sin\theta}$  select all the statements that are true

• The conic is symmetric about the y axis

• The conic is an ellipse

• The directrix is at x=7

• The focus is at the origin