The question given as a hyperbola equation. The question ask for the following information. 1. What is the half real axis of the hyperbola? 2. What is the half imaginary axis of the hyperbola? 3. What is the coordinate of the focus of the hyperbola? 4. What is the eccentricity of the hyperbola? 5. What is the asymptotes of the hyperbola?
When the focus of a hyperbola located in the x-axis, its standard equation is: x2/a2 – y2/b2 = 1 (a > 0, b > 0). The geometry property of a hyperbola is: 1. the graph of the hyperbola is outside these two lines, x = a, x = -a. 2. The hyperbola is symmetry to the x-axis, y-axis and the origin. 3. When the hyperbola intersect the axis, the distance between these two intersect points is called the real axis of the hyperbola that has the length of 2a and a is called the half real axis of the hyperbola. The coordinate of the vertex of the hyperbola is (-a, 0) and (a, 0). The length of the imaginary axis is 2b and b is the half imaginary axis. 4. Asymptotes is the extended lines of the two diagonals of the rectangle whose length is 2a and width is 2b. The graph of the hyperbola is pass through the vertex point and near the asymptotes and never cross the asymptotes.