Question

Help!

Answer 1

find an equation that models the hyperbolic path of a spacecraft around a planet if a= 107,124km and c=213,125.9 km

Answer 2

@phi

Answer 3

what is the equation for a hyperbola ?

Answer 4

is it x^2/a^2 - y^2/b^2

Answer 5

equals 1

Answer 6

oh ok, now what

Answer 7

any idea what they mean by c=213,125.9 km

Answer 8

no... not at all

Answer 9

You should look in your book, or google it. I found this
http://www.purplemath.com/modules/hyperbola.htm

do you see what c is ?

Answer 10

The important fact is
\[ a^2 + b^2 = c^2 \]
They told us a and c, so we can find b. once we know a and b, put them into the equation
can you find b ?

Answer 11

how do i do that

Answer 12

you start with
a^2 + b^2 = c^2

replace the letters (that you know) with their numbers.
what do you get when you do that ?

Answer 13

107,124^2+b^2= 213,125.9

Answer 14

close. it is c^2 on the right side

Answer 15

oops! ok whats next

Answer 16

solve for b^2: subtract 107,124^2 from both sides

Answer 17

106001.9

Answer 18

b^2=106001.9

Answer 19

c^2 - a^2 is a big number. did you square both before subtracting ?

Answer 20

no

Answer 21

you can type this into google to see what b^2 is
213,125.9^2 - 107,124^2 =

if we take the square root of it we will get b
sqrt (213,125.9^2 - 107,124^2)

Answer 22

you should be able to use a calculator to find this.

Answer 23

can you find b ?

Answer 24

33947097874.8

Answer 25

that is b^2
now take the square root to get b

Answer 26

184247.382274

Answer 27

ok, but we can round that to 184247.4

last step, replace a and b with their numbers in
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
I would not do the arithmetic and square the numbers, because they are so big.
just write them with the exponent 2

Answer 28

you get
\[ \frac{x^2}{107124^2} - \frac{y^2}{184247.4^2} = 1 \]

Answer 29

oh ok

Answer 30

thanks!

Answer 31

that is one ugly curve.

Answer 32

i bet! good thing i dont have to graph it !