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Chapter 10: Q. 15 (page 699)

In Problems 11-18, find an equation of the conic described. Graph the equation by hand.

Hyperbola; center at (-2,-3); focus at (-4,-3); vertex at (-3,-3)

Short Answer

Expert verified

The equation of the hyperbola is(x+2)21-(y+3)23=1

Step by step solution

01

Step 1. Given Information

Center of hyperbola at (-2,-3)

The focus of hyperbola at (-4,-3)

The vertex of the hyperbola is at (-3,-3)

02

Step 2. Calculation

Here, (伪,尾)=(-2,-3)

and (伪+ae,尾)=(-4,-3)

and(伪+a,尾)=(-3,-3)

03

Step 3. Calculation

Equating both sides we get

伪=-2,尾=-3

a=-1,e=2

Now, a2(e2-1)=(-1)2(22-1)

=3

Then the equation of the hyperbola is

(x+2)21-(y+3)23=1

04

Step 4. Graph

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