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3 years ago

How many foci does the graph of a hyperbola have

Mathematics

2 answers:

labwork [276]3 years ago

5 0

Answer:

A graph of a hyperbola have 2 foci.

Step-by-step explanation:

Foci of a Hyperbola-

The foci of a hyperbola are two fixed points located inside each curve of a hyperbola.

The foci is a plural of the word focus i.e. two focus of a hyperbola are combinely called foci.

Hence, a graph of a hyperbola have 2 foci.

Darina [25.2K]3 years ago

4 0

They Have 2: Like an ellipse, an hyperbola has two foci and two vertices; unlike an ellipse, the foci in an hyperbola are further from the hyperbola's center than are its vertices: The hyperbola is centered on a point (h, k), which is the "center" of the hyperbola. hope this helps c:

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Anika [276]

Answer:

Part a) $y=125x+23$

Part b) The graph of the equation for Aubrey's balance is parallel to the graph of Elijah's balance

Part c) Parallel graphs mean that their slopes are the same and that they deposited the same amount of $125 per week into their account balance during the summer.

Step-by-step explanation:

The correct question is

Elijah and Aubrey have summer jobs. Elijah deposits the same

amount of money in his account every week. The equation y = 125x + 72 represents his bank balance any given week of the summer. Aubrey also deposits the same amount into her account every week. At the end of the third week she has $398. At the end of the sixth week she has $773.

a. Write an equation to represent Aubrey's bank balance any given week of the summer.

b. Would the graph of the equation for Aubrey's balance be parallel to the graph of Elijah's balance? Explain.

c. What do the parallel graphs mean in terms of the situation?

Part a)

Let

x ----> the number of weeks

y ----> represent bank's balance

we know that

Elijah

$y=125x+72$ -----> equation A

Aubrey

we have the points

(3,398) and (6,773)

Find the slope m

$m=(773-398)/(6-3)$

$m=375/3$

$m=125$

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=125$

$point\ (3,398)$

substitute

$y-398=125(x-3)$ ----> equation in point slope form

Convert to slope intercept form

$y=mx+b$

$y-398=125x-375$

$y=125x-375+398$

$y=125x+23$ ----> Aubrey's bank balance

Part b)

Compare the equations

$y=125x+72$ ----> Elija's bank balance

$y=125x+23$ ----> Aubrey's bank balance

Remember that

If two lines are parallel, then their slopes are equal

In this problem the slopes are equal

$m=125\frac{\$}{week}$

therefore

The graph of the equation for Aubrey's balance is parallel to the graph of Elijah's balance

Part c) Parallel graphs mean that their slopes are the same and that they deposited the same amount of $125 per week into their account balance during the summer.

5 0

3 years ago