7. Consider the ellipse + =1, 0

2 7. Consider the ellipse + (a) Write down a set of parametric equations that describe the entire ellipse. Be sure to state the domain of your parametric equations. (Hint: Your parametric equations should involve trigonometric functions.) (b) The curvature -K of a curve C at a given 'point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvature K = O at every point. -For a curve C with parametric equations x = = y(t), then at the point y(t)) the Curvature can be calculated by USO SOui -parametric equationsffrcjiii (a) to calculate the curvature of the ellipse at Use your answev to (b) -to point(s) on the curve at which the curvature is maxi- mized. -Justifyyour answer with calculations. (d) Write 1-2 sentences explaining Whether your answer to (c) makes sense based on the illustration of the ellipse above.