**C4 Coordinate geometry Parametric curves**

SaaS analytics to help your company scale. All your SaaS business metrics in one place. Get started with just a click. Assumption: the coordinates of a point at time t are (x(t), y(t)). In some cases, you can manipulate the x and y functions into equations that do not require t. Example: x = cos(t... How can I determine where a parametric equation intersects itself? (self.learnmath) submitted 6 years ago If you have expressions for x(t) and y(t) you can use solving techniques to find a pair of values s,t with s!=t and . x(t)=x(s) y(t)=y(s) If in 3 dimensions, you get a third equation z(t)=z(s). As another approach, sometimes you can express your curve piecewise as functions of one of

**At what point does the curve intersect itself? Yahoo Answers**

more than one tangent line, because a parametric curve is allowed to intersect itself. Example Consider the curve de ned by the parametric equations x= t 2 ; y= (t 2 4)sint:... 27/03/2010 · The parametric curve x(t)=4cos(t) y(t)=5sin(2t) intersects itself at a point P=(x0y0) Find x0 and y0. What are the slopes of the 2 tangents at this point? Please show clear steps so that I can learn! Thank you so much!

**Parametric equations for a loop Physics Forums**

Then find minimum of D as a function of two independent parameters t1 and t2. If D at minimum is zero (or very close to zero), then these two lines intersect. Otherwise they just pass each other. If D at minimum is zero (or very close to zero), then these two lines intersect.... The parametric curve may not always trace out the full graph of the algebraic curve. We should always find limits on \(x\) and \(y\) enforced upon us by the parametric curve to determine just how much of the algebraic curve is actually sketched out by the parametric equations.

**How to find a self-intersection point of a parametric**

SaaS analytics to help your company scale. All your SaaS business metrics in one place. Get started with just a click. Assumption: the coordinates of a point at time t are (x(t), y(t)). In some cases, you can manipulate the x and y functions into equations that do not require t. Example: x = cos(t... Lasser [225] presents an algorithm to find all the self-intersection points of a Bezier curve by subdividing the Bezier polygon instead of the curve itself. Finally the self-intersection points are approximated by straight line intersections of the refined Bezier polygon.

## How To Find Where A Parametric Curve Intersects Itself

### Point where a parametric curve crosses itself? Yahoo Answers

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## How To Find Where A Parametric Curve Intersects Itself

### 242 Chapter 10 Polar Coordinates, Parametric Equations EXAMPLE 10.1.6 Graph r = 2sin?. Because the sine is periodic, we know that we will get the entire curve for values of ? in [0,2?).

- 3/04/2005 · The following parametric equations trace out a loop x = 8 - 3/2t^2 y = -3/6t^3+3t+1 1.) Find the t values at which the curve intersects itself. wouldn't i just have to solve for t for one of the equaltion to find t? also, can you find the intersects using a TI-83 plus to check your...
- 18/03/2010 · A curve is defined by parametric equations: x(t) = t^3 - 3t y(t) = t^2 - t If a graph of y vs. x is plotted, then the curve intersects itself at a point.
- As it turns out, there is an algorithm one can use, to derive the parametric equation of a torus-plane intersection curve. I discovered this a few nights ago, through my own exploration.
- 14/01/2008 · In this case, the curve will intersect itself once at the origin, given that 0 <= t <= 2*pi. Most parametric equations will also only intersect themselves if …

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