1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.

2) When determining the equation of a hyperbola you need the following:

a) does the hyperbola open up or to the right?

b) what is the center (h, k) of the hyperbola?

c) What is the slope of the asymptotes of the hyperbola?

3) The equation of a hyperbola is:

$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1$

(h, k) is the center of the hyperbola
± b/a is the slope of the line of the asymptotes
The equation starts with the "x" if it opens to the right and "y" if it opens up

5 0

3 years ago

Use the Distance Formula to find the distance between (13, 1) and (9,- 4), rounded to the nearest hundredth.

valina [46]

Answer:

about 6.40 units

Step-by-step explanation:

The distance formula is ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

For the given points, the distance between them is ...

d = √((9 -13)^2 +(-4-1)^2) = √((-4)^2 +(-5)^2) = √(16 +25)

d = √41 ≈ 6.40

The distance between the points is about 6.40 units.

4 0

3 years ago

Use the function f(x)=2x^3-3x^2+7 to complete the exercises

Anastaziya [24]

To answer this set of questions, all we have to do is just to substitute the value of x in F(x) to the given f(x) equation.

By substitution and following PEMDAS rule:
F(-1)=2(-1)³-3(-1)²+7=5

F(1)=2(1)³-3(1)²+7=6

F(2)=2(2)³-3(2)²+7=11

Therefore the answers are 5, 6 and 11.

8 0

3 years ago

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