FIRST NAME = L = 1,1

LAST NAME = M = 1,1

ALL INFORMATION GIVEN IS IN THE ATTACHMENT BELOW

For your discussion, first, create your parametric equations satisfying the criteria described. Using the chart below, the values for a, c (in that order) correspond to the first letter of your first name. The values for b, d (in that order) correspond to the first letter of your last name. ABCDEFG: 1, 0 HIJKLM: 1, 1 FRANCISCI MAVLOLYCI NOPQRST: 2, 0 UVWXYZ: 2, 1 CONICORVM APOLLONII PERGAEI Your values for a and b should be inserted into the appropriate parametric equations below. AD ILLVSTHISS SENATVM Historical Note: The 1654 edition of Conica by Apollonius of Perga [ (262 - 190 BC] edited by Francesco Maurolico. In this very influential book the terms such as parabola, ellipse, and hyperbola were first introduced. Ictd = To = (-2)" + 3sin(t) and yetd = yo = (-3)" + cos(t) Ectd = $1 = In(1 + at) and yetd = 1 = (t)+1 Tetd = $2 = 3 + (-t)" and yetd = yz = (-t) + a For example, if your name is Excelsior University, your first initial is E (a = 1, c = 0) and your last initial is U ( b = 2, d = 1), and these correspond to the following parametric equations to use for your main post. x1 = In(1 +t) and y1 = (t)3 Main Post Your main post should include the following: 1. State the parametric equations you will be presenting. 2. Find the equation for the tangent line at t = 0 to the curve represented by your parametric equations. Write the equation of the tangent line in two forms: (1) slope-intercept, and (2) using parametric equations. 3. Graph both sets of parametric equations (the curve and its tangent line) using Desmos - this will require some playing around on your part with the values for t for each curve. To learn more refer to the example of how to graph parametric equations in Desmos. B 4. Parametric equations are useful for describing the path of an object. Describe the direction of increasing t for your curve