Finding Cartesian equation of parametric surface.

Click For Summary
To find the Cartesian equation of the parametric surface defined by the equations x=2cos(t)cos(s), y=3sin(s), and z=sin(t)cos(s), the discussion suggests squaring each term and exploring the relationship between them. The user is unsure how to proceed after obtaining the squared terms and is considering whether constants α and β can be determined to express the equation in the form x² + αy² + βz² = constant. Additionally, the problem involves finding the equation of the tangent plane at the specific parameters S = 0 and t = π/2. The conversation highlights the need for clarity on the next steps in deriving the Cartesian equation and the tangent plane. Overall, the discussion revolves around transforming parametric equations into a Cartesian form and calculating the tangent plane.
Ral
Messages
11
Reaction score
0

Homework Statement


Find the Cartesian equation of the parametric surface: [2cos(t)cos(s), 3sin(s), sin(t)cos(s)]

Find eqn. of the tangent plane when S = 0, t = pi/2

Homework Equations


The Attempt at a Solution



I'm not quite sure what to do. All I've done is squared each term, which gave me.

4cos^2(t)cos^2(s)
9sin^2(s)
sin^2(t)cos^2(t)
 
Physics news on Phys.org
x=2\cos t\cos s

y=3\sin s

z=\sin t \cos s

Can't you find \alpha and \beta so that x^2+\alpha y^2 + \beta z^2= constant?
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Correct Parametrization for Calculating Area of a Tube?
  • · Replies 2 ·
Replies
2
Views
1K
Find the Cartesian equation given the parametric equations
  • · Replies 6 ·
Replies
6
Views
1K
Graph the Cartesian equation: x = 2 sin t, y = 4 cos t
  • · Replies 1 ·
Replies
1
Views
9K
Find the particular solution of the second order differential equation
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Solve a Differential Equation Using an Ansatz?
  • · Replies 5 ·
Replies
5
Views
2K
How should I use the averaging approximation to find this?
  • · Replies 3 ·
Replies
3
Views
2K
Calculating crossproduct integral, Parametrization
  • · Replies 5 ·
Replies
5
Views
2K
Graph the Cartesian equation: x=4t^2, y=2t
  • · Replies 2 ·
Replies
2
Views
3K
Length of the curve - parametric
  • · Replies 7 ·
Replies
7
Views
1K
How Does the Point of Tangency Move in Circular Motion?
  • · Replies 1 ·
Replies
1
Views
2K