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 $\frac{{(x + 2)}^{2}}{1} - \frac{{(y + 3)}^{2}}{3} = 1$

Step by step solution

Step 1. Given Information

Center of hyperbola at $(- 2, - 3)$

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

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

Step 2. Calculation

Here, $(α, β) = (- 2, - 3)$

and $(α + a e, β) = (- 4, - 3)$

and $(α + a, β) = (- 3, - 3)$

Step 3. Calculation

Equating both sides we get

$α = - 2, β = - 3$

$a = - 1, e = 2$

Now, $a^{2} (e^{2} - 1) = {(- 1)}^{2} (2^{2} - 1)$

$= 3$

Then the equation of the hyperbola is

$\frac{{(x + 2)}^{2}}{1} - \frac{{(y + 3)}^{2}}{3} = 1$

Step 4. Graph

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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

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

Step 4. Graph

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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

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Calculation

Step 4. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Pure Maths

Discrete Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

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 $(- 3, - 3)$