Friday

August 29, 2014

August 29, 2014

Posted by **Daniel** on Friday, December 16, 2011 at 12:36am.

x = 6sin(t), y = t^2 + t; (0,0)

How do I do this without the value of t? I don't see a way to eliminate the parameter.

- calculus -
**Daniel**, Friday, December 16, 2011 at 12:46amOh also if you can, how do you find d2y/d2x for parametrics?

- calculus -
**Steve**, Friday, December 16, 2011 at 1:01pmThe nice thing about parametric equations is that you don't have to eliminate the parameter.

dy/dx = dy/dt / dx/dt

dy/dx = (2t+1)/6cos(t)

This is zero at t = -1/2 and has a vertical asymptote whenever t = an odd multiple of pi/2.

The graph is a kind of double wave sine surve. It wanders back and forth in the x direction, but the escillations get longer in the y direction, since y uses t^2, instead of just t.

Mosey on over to wolfram dot com to see the big picture. Type in a command like

graph x=6*sin(t), y=t^2 + t, t=-5..5

try

graph x=6*sin(t), y=t^2 + t, t=-2..1.5 to see the horizontal tangent at t=-1/2

**Related Questions**

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

math - With regards to question J: The variables x and y are connected by the ...

calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...

calculus - 1. Given the curve a. Find an expression for the slope of the curve ...

calculus - Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx...

12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...

maths - given the equation of the curve as y=8-2x^2 (a) find equations of ...

Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...

Help Calc.! - original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1...

calculus - A curve passes through the point (1,-11) and it's gradient at any ...