Question

Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below?

(x-2)^2/4+(y+5)^2/9=1
A. (-5,5) and (-5,-1)
B. (0,-5) and (4,-5)
C. (5,5) and (-1,-5)
D. (2,-2) and (2,-8)

Answer 1

HI!!!

Answer 2

do you know what conic section this is?

Answer 3

I think a hyperbola

Answer 4

nope

Answer 5

because it has a plus sign between the two terms, not a minus sign, it is not a hyperbola

Answer 6

Ohh okay

Answer 7

so what is it?

Answer 8

ellipse

Answer 9

right
and what is the center of this ellipse?

Answer 10

Im not sure but I think 4

Answer 11

oh no the center is a point in the plane, an ordered pair \((h,k)\) not a number

Answer 12

your ellipse is written in standard form \[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] center is \((h,k)\)

Answer 13

(-2,5)

Answer 14

hmm close but no

Answer 15

would it be (2,-5)

Answer 16

\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\
\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1\]

Answer 17

yes \((2,-5)\)

Answer 18

we need to know all these things to get the answer, i am not asking just to waste your time
now we need to know two more things

Answer 19

the second one

Answer 20

yes, and now we are just about done

Answer 21

because we know the center is \((2,-5)\) and we know the major axis is vertical, so the first coordinates of both endpoints of the major axis will lie ABOVE and BELOW \((2,-5)\)

Answer 22

that means this

Answer 23

we did not even have to find that they are 3 units above and below \((2,-5)\) because you only had one answer choice where the first coordinate was 2

Answer 24

I think it would be A based off of that

Answer 25

we could find the 3 if you like

Answer 26

A???

Answer 27

yes is that not right?

Answer 28

i will let you look at the answer choices and the answer i wrote above and figure out which one it is for yourself