How do I put this in a regular hyperbola form?

Question

I am given:
 x^2 - 4y^2 = 1. 

I need to say which conic section it is (circle, parabola, ellipse, hyperbola). I am 99% sure it's a hyperbola. 

I need it to be in the standard form of a hyperbola equation, which is:
{ (x-h)^2 / a^2 } - { (y-k)^2 / b^2 } = 1

I am having a lot of trouble figuring this out. I need to get rid of the 4 in front of the y, and keep the 1 by itself on the right side. I am pretty sure that this hyperbola is centered around (0,0), so h and k are both 0.

Please help if you can! Thank you.

DWRead · Accepted Answer

x² - 4y² = 1
The signs are different, indicating a hyperbola.

You need to move the 4 to the denominator, without changing the right-hand side. 

Remember that dividing by a fraction is the same as multiplying by the upside-down fraction, so
y²/(1/4) = (4/1)y²
1/4 = (1/2)²

The equation of the hyperbola is
x² + y²/(1/2)² = 1
vertex (0,0)
http://www.flickr.com/photos/dwread/2799463319/

Ron W · Answer

Yes, it is a hyperbola.

Write 4y² as y²/¼ Then the standard form is

x² - {y²/½² } = 1

or in its full glory

{(x-0)² / 1²} - {(y-0)² / (½)²} = 1

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How do I put this in a regular hyperbola form?

2 Answers