# Tagged Questions

For questions about parametric equations, their application, equivalence to other equation types and definition.

2answers
44 views

### How to compute $\int_0^2(1+4t^2+9t^4)^{1/2}\text{d}t$?

The original question was: find the length $\ell$ of the curve $\gamma$ given the parametric equations: $$x=t~~~~~ y=t^2~~~~~ z=t^3$$ from $t=0$ to $t=2$
1answer
14 views

### Rectangular Hyperbola - Eliminating the Parameter

Question: The point P (2p,2/p) lies on the rectangular hyperbola C with equation xy = 4. (a) Find the equation of the normal to C at P. The normal at P meets C again at the point Q. The mid-point ...
2answers
36 views

### Speed of a parametric function?

I know speed = |velocity| Why is speed of parametric defined as $$speed = \sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}$$ How is this derived? What is the principle here? Is ...
2answers
42 views

### Why is $\cos\left(\frac{3\pi}{2}-t+2k\pi\right) = -\sin(t)$ [on hold]

Why is this true? $$\cos\left(\frac{3\pi}{2}-t+2k\pi\right) = -\sin(t)$$
1answer
30 views

### parametric equations, finding the range of t

When parametrizing a curve how doe we obtain the range of $t$? For example lets say we have the parametrization: $x(t) = 1+3t$ and $y(t) = 2+5t$. How do we find the range of t? $t\to[?,?]$
0answers
22 views

### Parameterization which is closed under addition

Suppose $\beta_1(t)$ and $\beta_2(t)$ are two parametric curves defined on $[0,1]$. Let $\beta_1^*(t)$ and $\beta_2^*(t)$ are two re-parametrized of the above curves. Now, I looking for a ...
0answers
25 views

### Parametrisation of the curve after a short time

I am trying to wrap my head around this differential geometry problem. I am given velocity V with components in the principle normal and binormal directions. Then I am given an approximation of the ...
0answers
27 views

### Rotating a 2d equation in a 3d space? [closed]

I'm attempting to rotate a shape taken from a parametric equation. I'm doing this inside a Java program, so it automatically adjusts the variables as I need. I have: $t = \pi$ but t decreases in ...
0answers
21 views

1answer
26 views

### Find the parametrization of the curve resulting from intersection of two surfaces

The question reads as follows: Find a parametrization of the curve resulting from the intersection of the surfaces: $z = x^2 - y^2$ and $z= x^2 +xy - 1$ My attempt: (Use y = t as a parameter, so ...
0answers
29 views

2answers
38 views

### How to use parametric equation/trigonometric identity to show an ellipse?

I have the equation $16x^2+25y^2=400$, and the parametric equation $(x,y)=(5\cos t, 4\sin t)$. If I plug in the parametric equation into the first equation, I end up with the trigonometric identity ...
6answers
102 views

### If $a^2 + b^2 = 1$, show there is $t$ such that $a = \frac{1 - t^2}{1 + t^2}$ and $b = \frac{2t}{1 + t^2}$

My question is how we can prove the following: If $a^2+b^2=1$, then there is $t$ such that $$a=\frac{1-t^2}{1+t^2} \quad \text{and} \quad b=\frac{2t}{1+t^2}$$
2answers
54 views

### Calculus problem of finding the equation of a line.

Find the equation of a line that passes through the origin, with positive slope, and its tangent to the parabola given by :$y = x^2 - 2x + 2$ My approach to this problem was to differentiate the ...
2answers
59 views

### Parametric Trig Functions

A closed curve in the $(x, y)$-plane is represented by the functions $$x(θ)=\frac12(\cos \theta +\sqrt2 (\sin \theta))$$ $$y(θ)=\frac12(− \cos \theta +\sqrt2 (\sin \theta))$$ where the parameter ...
2answers
43 views