Question

What are the vertices of the hyperbola given by the equation?

Answer 1

first you need to find the center of the hyperbola. do you know what this is?

Answer 2

do you know how to find the center of a hyperbola?

Answer 3

Not exactly? can you show me :)

Answer 4

the standard form of a hyperbola is (check image attached)

where (h, k) is the centre.

Answer 5

so in this case what will be our centre if you compare it to your hyperbola equation?

Answer 6

wait am i getting the values for the variables from the original? :/

Answer 7

we are trying to get to find the vertices. you have your hyperbola equation. so i gave you the standard form of a hyperbola. to find the vertices, first we find the center. which is (h,k) from the standard form of a hyperbola that i gave you. so now compare this to YOUR hyperbola equation and get the centre (h,k). do you understand now?

Answer 8

-5,-8?

Answer 9

no. close. but wrong answer. the center is (5, 8)

Answer 10

so now that we have the center (h,k). for your hyperbola. the vertices will be (h + a, k) and (h - a, k). So now if you work this out. you can find the vertices of your hyperbola :)

Answer 11

(5+9,8) and (h-9,8)?

Answer 12

(5+9,8) and (5-9,8)? **

Answer 13

no. first what is the value of a?

Answer 14

look carefully at the denominator of the x term. it's \[a ^{2}\]. but we are interested in \[a\]

Answer 15

9?

Answer 16

no. \[a ^{2} = 9\]

Answer 17

what now then will be our value for \[a\]
?

Answer 18

3?

Answer 19

nice. so now find (h + a, k) and (h - a, k) which will be our vertices for this hyperbola :)

Answer 20

5+3, 8) and (h-3, 8)?

Answer 21

good. but what is the value of \[h\]?

Answer 22

comparing to the standard form of the hyperbola?

Answer 23

5+3, 8) and (5-3, 8)?

Answer 24

super! so now write it well as points. get rid of the "+" sign

Answer 25

2,8 and 8,8?:)

Answer 26

can you find this in the possible answers? if you can, that's your answer ;)

Answer 27

thankkks!

Answer 28

its A :)

Answer 29

you're welcome ;)