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Chapter 10: Q 12. (page 683)

Identify the conic that each polar equation represents. Also, give the position of the directrix

r=68+2sin(胃)

Short Answer

Expert verified

This polar equation is a hyperbola.

The equation of directrix isy=3

Step by step solution

01

Step 1. Given information

The polar equation is

r=68+2sin(胃)

02

Step 2. Finding e and p

The polar equation is

r=68+2sin(胃)

Divide top and bottom by 8

r=6888+28sin(胃)r=381+14sin(胃)

Compare with the standard polar equation

r=ep1+esin(胃)

So,

role="math" localid="1647172232733" ep=34e=1414脳p=34p=3

03

Step 3. Identify the conic equation

We have got

e=14<1

So, this is an ellipse equation.

04

Step 4. Finding the directrix equation

The formula for the directrix equation is

y=p

Plug value p=3

So, the directrix equation isy=3

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Most popular questions from this chapter

Whispering Gallery: A hall 100feet in length is to be designed as a whispering gallery. If the foci are located 25feet from the center, how high will the ceiling be at the center?

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

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Vertex at 0,0, axis of symmetry is the x-axis; containing the point2,3.

In Problems 19鈥�28, find an equation for the hyperbola described. Graph the equation by hand. Center at (0,0); focus at (3,0); vertex at(1,0).

In Problems 31鈥� 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21鈥�30 for Problems 31鈥� 40.

3x2-10xy+3y2-32=0
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