Open the “Hyperbola” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB. Check the boxes “Show Hyperbola” and “Show Equation of Hyperbola.”

(a) Set the value of a to 2. Move F₁ to (2, 2) and F₂ to (2, −4). Look at the equation of the hyperbola and note the center. The transverse axis is the line through the vertices, foci, and center. What is the equation of the transverse axis?

(b) Move F₁ to (−4, −4). Look at the equation of the hyperbola and note the center. What is the value of c, the distance from the center to either focus?

(c) Leave the value of a at 2. Move F₁ to (−6, −1) and F₂ to (2, −1). Look at the equation of the hyperbola and note the center. If the transverse axis is parallel to the x-axis, then the equation of the hyperbola is of the form

(d) If the transverse axis is parallel to the y-axis, then the equation of the hyperbola is of the form

Transcribed Image Text:

● (xh)² a² (y - k)² a² (y - k)² b² = 1 (x - h)² = 1 b²