Question

A hyperbola has vertices of (+-5,0) and one focus (6,0). What is the standard-form of equation of the hyperbola?

Answer 1

is it:\[\frac{ x^2 }{ 25 }+\frac{ y^2 }{ 36 }=1\] or am I completely off?

Answer 2

@iGreen @SolomonZelman @satellite73

Answer 3

Can anyone help?..

Answer 4

@AlexandervonHumboldt2

Answer 5

@satellite73

Answer 6

for hyperbolas c^2 = a^2 + b^2

you're given c = 6, a = 5

Answer 7

find the value of \(b\) and plug in
\[\dfrac{x^2}{a^2}\color{red}{-}\dfrac{y^2}{b^2}=1\]

Answer 8

ohhhh.. I think I so wrote that wrong.

Answer 9

\[b=\sqrt11\]

Answer 10

yep

Answer 11

so it's \[\frac{ x^2 }{ 25 }+\frac{ y^2 }{ 11 }=1\]

Answer 12

right?

Answer 13

careful about the sign in between

Answer 14

it should be
\[\frac{ x^2 }{ 25 }\color{red}{-}\frac{ y^2 }{ 11 }=1\]

Answer 15

ohhh right. I keep messing that up.

Answer 16

why's it a minus sign and not a plus sign?

Answer 17

+ sign for ellipses
- sign for hyperbolas

there is a reason why this is so.. look up definition of hyperbola and ellipse

Answer 18

okay... thanks. :)

Answer 19

http://mathworld.wolfram.com/Hyperbola.html

Answer 20

lookup ellipse also
http://mathworld.wolfram.com/Ellipse.html

Answer 21

thanks :)