Question

The vertices of the following graph are at (-2, 0) and (2, 0) True or False! I say True

Answer 1

@Michele_Laino i say True

Answer 2

that's right! It is true, since they are the vertices of an hyperbola

Answer 3

@Michele_Laino i said false for this

Answer 4

here we have:
c=sqrt(13), so c^2=13
furthermore, from your data, I can write:
a=2, and b=3. Now the subsequent equation holds (in general):
\[\Large {c^2} - {a^2} = {b^2}\]

Answer 5

substituting our numeric values, for a, b, and cwe get:
\[\Large {c^2} - {a^2} = 13 - 4 = 9 = {b^2}\]

Answer 6

so, what is the answer?

Answer 7

9 correct

Answer 8

@Michele_Laino

Answer 9

so the answer is false to my question since it equals 9

Answer 10

then the answer is true, since our identity is checked!

Answer 11

@Michele_Laino thanks,

Answer 12

@Michele_Laino

Answer 13

it would be A @Michele_Laino

Answer 14

sorry, I have made an error of sign, the right equation, is:
\[\Large \frac{{{y^2}}}{{{a^2}}} - \frac{{{x^2}}}{{{b^2}}} = - 1\]

Answer 15

sorry again, the right equation is:
\[\Large \frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = - 1\]
with a=5, and b=3

Answer 16

so, waht is the right option?

Answer 17

@Michele_Laino so the answer would be A ?

Answer 18

that's right! Since if we set x=0, we get y=+3 and y=-3
and they are the points of intersection of our hyperbola with the y-axis:
(0,3) and (0,-3)

Answer 19

@Michele_Laino i said false since the center is 1,-3 correct?

Answer 20

that's right!

Answer 21

@Michele_Laino

Answer 22

here we have a=sqrt(2), and b=2, so we have to apply this equation:
\[\Large \frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = - 1\]
please what equation do you get, after the substitution of a and b?

Answer 23

@audicolen

Answer 24

@Michele_Laino 2 and 4

Answer 25

so the answer would be a @Michele_Laino

Answer 26

ok! so we get this equation:
\[\frac{{{x^2}}}{2} - \frac{{{y^2}}}{4} = - 1\]

Answer 27

yes

Answer 28

nevertheless it is not the requested equation, since, our hyperbola is traslated (from the position whose center is located at the origin of the coordinate system) by 1 unit towards right and 3 units down, so our equation has to contain the subsequent quantity:
x-1,
and
y-3.
So, waht is the right option?

Answer 29

oops! y+3, not y-3

Answer 30

@Michele_Laino so the correct equation is C

Answer 31

that's right!

Answer 32

@Michele_Laino i said true for this

Answer 33

that's right! Your answer is correct!

Answer 34

last ones

Answer 35

question #7
here we have:
a=5, and b=6
furthermore, we have to apply this formula:
\[\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = - 1\]
So, what is the right option

Answer 36

oops! the right equation is:
\[\Large \frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1\]

Answer 37

with a=5, and b=6, so:
a^=25, and b^2=36

Answer 38

@Michele_Laino so the anser would be D

Answer 39

that's right!

Answer 40

question #8
here we have:
a=4, and c=5
so we have to apply this formula:
\[{c^2} - {a^2} = {b^2}\]

Answer 41

we have:
\[{b^2} = 25 - 16 = ...?\]
what is b^2 ?

Answer 42

9

Answer 43

@Michele_Laino so the correct answer is A

Answer 44

ok! so what is your option, keep in mind that we have to apply the same formula as before:
\[\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1\]

Answer 45

That's right! Your answer is option A

Answer 46

question #9

Answer 47

number 9 is B i believe

Answer 48

we have a=3, and b=5, furthermore, we have to apply the same formula, as before:
\[\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1\]
so, what is the right option?

Answer 49

@Michele_Laino its B

Answer 50

that's right! The right option is option B

Answer 51

@Michele_Laino The symmetry of a hyperbola with a center at (h, k) only occurs at y = k true or false. i said false

Answer 52

if the axis of our hyperbola is parallel to the x-axis, then the answer is true