1. Math
2. Geometry
3. consider a plane curve c given by the parametric equations...

# Question: consider a plane curve c given by the parametric equations...

###### Question details

Consider a plane curve C given by the parametric equations x(t) = 6t2 and y(t) = 3t3 − 4t. Note: In the solution of this problem use symmetry wherever possible.

1. (a) Find the point A(x0,y0) where C crosses itself. Hint: Solve the system of equations 6t21 = 6t22 and 3t31 − 4t1 = 3t32 − 4t2.

2. (b) Find equations of both tangents at A.

3. (c) Find the points on C where tangent is horizontal or vertical.

4. (d) Determine where C is concave upward or downward.

5. (e) Indicate by arrows the direction of C.

6. (f) Find the area enclosed by the loop. Hint: Look at the problem 77 in the section 10.3

of the textbook. Note: If you integrate the loop counterclockwise, the integral will be

negative. Take absolute value of your answer.

7. (g) Find the arc length of the loop.