Chapter MPS, Problem 10.7MPS

a.

To determine

To identify the vertices, foci and asymptotes of the hyperbola.

Explanation of Solution

Given:

Two bats are $300$ feet apart and swarm is $80$ feet farther from the first bat than the second bat.

Calculation:

The equation of the hyperbola can be described as follows-

So, according to the question-

  $\frac{{(x-80)}^2}{300}+\frac{{(y-380)}^2}{300}=1$

Now comparing the above equation with

  $\frac{{(x-h)}^2}{a^2}+\frac{{(y-k)}^2}{b^2}=1$

Therefore, the coordinates of center $(1,-3)$ , and lengths of major axes $2a=2\cdot 4=8$ and minor axes of the ellipse is $2b=2\cdot 2=4$ .

The foci is

  $\begin{array}{l}{c}^2=16-4\\ c=\sqrt{12}=2\sqrt{3}\end{array}$

The foci is $(4,2\sqrt{3})(4,-2\sqrt{3})$

b.

To determine

To write the equation.

Answer to Problem 10.7MPS

  $\frac{{(x-80)}^2}{300}+\frac{{(y-380)}^2}{300}=1$

Explanation of Solution

Given:

Two bats are $300$ feet apart and swarm is $80$ feet farther from the first bat than the second bat.

Calculation:

The equation of the hyperbola can be described as follows-

So, according to the question-

  $\frac{{(x-80)}^2}{300}+\frac{{(y-380)}^2}{300}=1$