# Introduction to Parametric Equations - Page 6

Questions

- How do you find the parametric equations for the line through the point P = (4, -4, 1) that is perpendicular to the plane 3x + 1y - 4z = 1?
- How do you find the set of parametric equations for the line in 3D described by the general equations x-y-z=-4 and x+y-5z=-12?
- What is the parametric equation of an ellipse?
- For #f(t)= (t^3-t^2+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?
- How do you find the parametric equations for a line through a point?
- How do you find parametric equations for the path of a particle that moves along the #x^2 + (y-3)^2 = 16# once around clockwise, starting at (4,3) 0 ≤ t ≤ 2pi ?
- Given x(t)=3sin(t) - 3, y(t)=t-1 for 0 is less than or equal to t is less than or equal to 2pi How do you find the velocity of the particle at t=3?
- How do you find the parametric equation of a parabola?
- What is #r sin theta = 5# in #(x,y)# coordinates ?
- How do you find parametric equations and symmetric equations for the line through t0 and parallel to the given line t0 = (4, -2, 4) and x + 1 = y/2 = z + 5?
- Eliminating the parameter in the parametric equations x = 5 - 3t, y = 2+t yields what equation?
- How do you find parametric equations for the path of a particle that moves around the given circle #x^2 + (y – 2)^2 = 4# clockwise, starting at (2, 2)?
- How do you determine the parametric equations of the path of a particle that travels the circle: #(x−3)^2+(y−1)^2=9# on a time interval of #0<=t<=2#?
- For #f(t)= (t+21,-3t^2-2t)# what is the distance between #f(2)# and #f(5)#?
- How do you find parametric equations and symmetric equations for the line through #(3, −2, 5)# and parallel to the line #x + 3 = y/2 = z − 2#?
- What are parametric equations used for?
- What is the parametric equation of the line through (1,1,1) that is parallel to i+j+k?
- Let #x = e^t + 3# and #y = e^(2t)+6e^t+9# how do you eliminate the parameter and write y in terms of x?
- How do you find parametric equation for the line through the point P(-7,-3,-6) and perpendicular to the plane -2x + 2y + 6z =3?
- How do you determine the vector and parametric equations for the plane through point (1, -2,3) and parallel to the xy-plane?