Basics of a hyperbola in conics form

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properties of a hyperbola
$-(\frac{x-6}{4})^2 + (\frac{y+5}{3})^2=1$ $- (\frac{x - 6}{4})^{2} + (\frac{y + 5}{3})^{2} = 1$
1. Identify the type of conic section.
2. State the "center".
3. Set up the guidelines for the conic graph.
4. Find the "vertices".
5. Locate the "foci".
6. Find the "eccentricity".
7. Find the equations of the "asymptotes".
8. Find the lengths of transverse axis and conjugate axis.

hyperbola: the difference of the distances from any point on a hyperbola to each focus is constant and equal to the transverse axis

2a

.
ellipse: the sum of the distances from any point on an ellipse to each focus is constant and equal to the major axis

2a

c= \sqrt{a^2 - b^2}

c

: distance from the center to a focus

e= \frac{c}{a}

e

: eccentricity; the larger the value of

e

, the straighter the hyperbola

Conics - Hyperbola