Question

Write the equation of the conic section with the given properties

A hyperbola with vertices (0,-6) and (0,6) and asymptotes y=3/4x and y=-3/4x

Answer 1

@jim_thompson5910

Answer 2

let me think

Answer 3

how far did you get with this?

Answer 4

Nowhere

Answer 5

what is the midpoint of (0,6) and (0,-6) ?

Answer 6

0

Answer 7

Or (0,0)

Answer 8

(0,0) yes

Answer 9

what is the distance from (0,0) to (0,6)

Answer 10

6

Answer 11

so a = 6

'a' is the distance from the center (0,0) to either vertex

Answer 12

to find b, we need to solve this equation

a/b = 3/4

Answer 13

a = 6, so

a/b = 3/4
6/b = 3/4

what is the value of b?

Answer 14

7?

Answer 15

6/b = 3/4
6*4 = b*3 ... cross multiply
24 = 3b
3b = 24
b = ?????

Answer 16

8

Answer 17

b = 8 is correct

Answer 18

(h,k) is the center, so (h,k) = (0,0)

h = 0 and k = 0

Answer 19

a = 6
b = 8
h = 0
k = 0

plug those values into
\[\Large \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\]

Answer 20

\[\frac{ (y-0)^2 }{ 6^2 }-\frac{ (x-0)^2 }{ 8^2 }\]

Answer 21

=1

Answer 22

yes

Answer 23

Ok, and would I do the same thing for the Ellipse except with the Ellipse formula?

Answer 24

ellipses don't have asymptotes though

Answer 25

then how would I solve it if it were an Ellipse and it asked for a minor or major axis?

Answer 26

I'd have to see the full problem

Answer 27

Like this: Write the equation of the conic section with the given properties
an Ellipse with vertices (0,-5) and (0,5) and a minor axis of length 8

Answer 28

what is the distance from (0,-5) to (0,5) ?

Answer 29

10?

Answer 30

yes, half of this distance is 5

half of the minor axis (8) is 4

so for

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

we know that

h = 0
k = 0
a = 4
b = 5

Answer 31

\[\frac{ (x-0)^2 }{ 4^2 }+\frac{ (y-0)^2 }{ 5^2 }=1\]

Answer 32

yeah

Answer 33

Ok, thank you

Answer 34

no problem