A conic section is a curve obtained by the intersection of the surface of a cone with a plane. A conic section can be a circle, a hyperbola, a parabola, and an ellipse.
For a circle, the general equation of a circle with center, (a, b), and a radius, r, is of the form
![(x-a)^2+(y-b)^2=r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%2B%28y-b%29%5E2%3Dr%5E2)
For a hyperbola, the general equation of a hyperbola with center (h, k), and a and b half the lengths of the major and the minor axis respectively is of the form.
![\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} =1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%20-%20%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%20%3D1)
For a parabola, the general equation of a parabola with center (h, k), and a multiplier a is of the form
![y-k=a(x-h)^2](https://tex.z-dn.net/?f=y-k%3Da%28x-h%29%5E2)
For an ellipse, the general equation of an ellipse with center (h, k), and a and b half the lengths of the major and the minor axis respectively.
![\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%20%2B%20%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%20%3D1)
Given the equation
![x^2-9y^2=900](https://tex.z-dn.net/?f=x%5E2-9y%5E2%3D900)
It can be rewritten as
![\frac{(x-0)^2}{900} - \frac{(y-0)^2}{100} =1 \\ \\ \frac{(x-0)^2}{30^2} - \frac{(y-0)^2}{10^2} =1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-0%29%5E2%7D%7B900%7D%20-%20%5Cfrac%7B%28y-0%29%5E2%7D%7B100%7D%20%3D1%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B%28x-0%29%5E2%7D%7B30%5E2%7D%20-%20%5Cfrac%7B%28y-0%29%5E2%7D%7B10%5E2%7D%20%3D1%20)
This gives an equation of a hyperbola with center (0, 0), half the length of the major axis = 30 and half the length of the minor segment = 10.
The domain of the equation is all real values of x.