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
[tex](x-a)^2+(y-b)^2=r^2[/tex]
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.
[tex] \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} =1[/tex]
For a parabola, the general equation of a parabola with center (h, k), and a multiplier a is of the form
[tex]y-k=a(x-h)^2[/tex]
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.
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1[/tex]
Given the equation
[tex]x^2-9y^2=900[/tex]
It can be rewritten as
[tex] \frac{(x-0)^2}{900} - \frac{(y-0)^2}{100} =1 \\ \\ \frac{(x-0)^2}{30^2} - \frac{(y-0)^2}{10^2} =1 [/tex]
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.
