Question

At what points does the curve r(t) = ti (9t − t²)k intersect the paraboloid z = x² + y²

Answer 1

To find the points of intersection between the curve r(t) = ti (9t − t²)k and the paraboloid z = x² + y², you need to substitute the values of x, y, and z from the curve equation into the paraboloid equation.

Step-by-step explanation:

To find the points of intersection between the curve r(t) = ti (9t − t²)k and the paraboloid z = x² + y², we need to substitute the values of x, y, and z from the curve equation into the paraboloid equation.

Let's solve this step by step:

1. Substitute x = t, y = t(9t − t²), and z = t² + t²(9t − t²)².
2. Simplify the equation and express it in terms of t.
3. Find the values of t that satisfy the equation and substitute them back into the curve equation to obtain the corresponding points of intersection.