Develop the parametric equations of a hyperbola by following these steps.
a. Write the equation of a unit hyperbola in standard form using x and y.
b. Replace x with 1 / cos t and solve for y in terms of t. You should get a square root equation.
c. Add the terms under the radical by finding a common denominator.
d. Use the identity (sin t)2 + (cos t)2 = 1 to rewrite the numerator under the radical.
e. Use the identity tan t = sin t / cos t to rewrite the equation.
f. State the parametric equations for a unit hyperbola. (Look back at 16a to determine the parametric equation for x.)
g. Modify the parametric equations in 16f to incorporate horizontal and vertical translations (h and k) and horizontal and vertical scale factors (a and b).