A Hyperbola is a locus point which moves in a plane such that its distance from the fixed point to the distance from the fixed line has a constant ratio > 1. The two fixed points are called the focii. The constant ratio is the eccentricity and is given by e. It is given by the equation
Hyperbola equation

Hyperbola Calculator is an online tool which calculates the focii, eccentricity and the asymptotes. Provided are the blocks where you are supposed to enter the center coordinate points and the a and b values to get the answer.

Hyperbola Diagram
The Equations of Hyperbola are

Focus F in X Coordinate = xo + $\sqrt{a^{2} + b^{2}}$
Focus F in Y Coordinate = yo
Focus F' in X Coordinate = xo - $\sqrt{a^2 + b^2}$
Focus F' in Y Coordinate = yo
Asymptotes L'H y = $\frac{b}{a}$ x + yo - $\frac{b}{a}$ xo

                            
LH' = - $\frac{b}{a}$ x + y0 + $\frac{b}{a}$ x0

Eccentricity = $\frac{\sqrt{(a^{2} + b^{2})}}{a}$.

Let us analyze the method to solve the Hyperbola

Step 1 : Read the problem and observe whether it is of the form

$\frac{(x− x_{0})^2}{a^{2}}$ + $\frac{(y − y_{0})^2}{b^2}$ = 1.

where (a,b) are the points from center of hyperbola.

Step 2 :  Calculate the hyperbola parameters using the above formula based on desired values. Substitute the values in the formula to get answer.