Question

Can someone help me with two questions in conic sections.

Answer 1

1. What is the equation of the following graph?

Answer 2

2. What are the foci of the following graph?

Answer 3

i hyperbola has the equation \(\Large \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)
so you need to find a and b

Answer 4

how do I find a and b?

Answer 5

you see that box
a is half way from right to left
b is half way from bottom up

Answer 6

so you just take the length of that rectangle
and divide into half

Answer 7

2b=8 so b=4
2a=6 so a=3

Answer 8

okay thank you! so the first problem is \[\frac{ x ^{2} }{ 3^{2} }-\frac{ y ^{2} }{ 4^{2} }=1\]

Answer 9

yes !

Answer 10

Can you also help with the 2nd problem

Answer 11

to find the foci
you need to find a and b again
then use b^2+c^2=a^2
c=sqrt{a^2-b^2}
c is the distance from the foci
to the center of that rectangle

Answer 12

that will get you the coordinates of the foci

Answer 13

you will find b and a the same way we just did

Answer 14

I got A=2 and B=5 is that correct?

Answer 15

yes!

Answer 16

okay what do I do next?

Answer 17

well i said c is the distance from center to foci
so what do you think any idea

Answer 18

actually an error
\(c=\sqrt{a^2+b^2}=\sqrt{29}\)
the foci has coordinates (0,c)

Answer 19

so c=5.39?