Problem 3. (Python, 15 points) a) Plot the astroid curve defined Astroid parametrically: 3 I(t) = (a - b) cost + bcos((a/b - 1)t) N y(t) = (a -b) sint - bsin((a/b - 1)t) 1 0 Ask user to enter a value of 'b' -1 Define a=4b Generate values of x and y for -2 values of t from 0 to 2nt with -3 At= TC 150. Plot y vs. x using a red solid line. " Include a title ' Astroid' and x, y -2 N . X axes' labels. b) Write a text file "curve.txt" that contains all of the x, y values created part a) and looks like the following (the dots '...' indicate missing valu This file contains points x, y on a curve. 0.0 0 . 0 0 .5 0 . 996 ... -20.2 2.345

Problem 3. (Python, 15 points) a) Plot the astroid curve defined parametrically: r(t) = (ab) cost+ bcos((a/b 1)t) y(t)= (a - b) sint - bsin((a/b 1)t) Ask user to enter a value of 'b' Define a=4b Generate values of x and y for values of t from 0 to 2 with At= /50. Plot y vs. x using a red solid line. Include a title 'Astroid' and x, y axes' labels. y 3 -20.2 2.345 2 1 0 -1 -2 -3 -4 -4 -2 Astroid This file contains points x, y on a curve. 0.0 0.0 0.5 0.996 OX 0 b) Write a text file "curve.txt" that contains all of the x, y values created part a) and looks like the following (the dots ..' indicate missing value 2