# Introduction to Parametric Equations - Page 5

Questions

- How do you find the (shortest) distance from the point P(1, 1, 5) to the line whose parametric equations are x = 1 + t, y = 3 - t, and z = 2t?
- What is the area bounded by the parametric equations? : # x=acos theta # and # y=bsin theta #
- How do you find parametric equations and symmetric equations for the line through the points (1, 3, 2) and ( -4, 3, 0)?
- How do you find a parametric equation for a particle moving twice counter-clockwise around the circle #(x-2)^2 + (y+1)^2 = 9# starting at (-1,-1)?
- For #f(t)= (1/(2t-3), te^t )# what is the distance between #f(0)# and #f(1)#?
- Consider the parametric equation: #x = 15(cos(theta) + (theta)sin(theta))# and #y = 15(sin(theta) - (theta)cos(theta))#, What is the length of the curve for #theta = 0# to #theta = pi/8#?
- How do you find parametric equations for the line through P-naught=(3,-1,1) perpendicular to the plane 3x+5y-7z=29?
- Consider the parametric equation #x = 9(cost+tsint)# and #y = 9(sint-tcost)#, What is the length of the curve for #t= 0# to #t=3pi/10#?
- For #f(t)= (sqrt(t+2)/(t+1),t^2+3t)# what is the distance between #f(0)# and #f(2)#?
- How do you write the parametric equations represent the ellipse given by #x^2/9 + y^2/81=1#?
- For #f(t)= (sint,cost)# what is the distance between #f(pi/4)# and #f(pi)#?
- For #f(t)= (sin^2t,t/pi-2)# what is the distance between #f(pi/4)# and #f(pi)#?
- How do you convert each parametric equation to rectangular form: #x = t^(3/2) + 1#, #y = sqrt{t}#?
- How do you find parametric equations for the line which passes through the point (1,−2,3) and is parallel to both of the planes 3x + y + 5z = 4 and z = 1 − 2x?
- For #f(t)= (te^(t-1),t^2-t+1)# what is the distance between #f(0)# and #f(2)#?
- The motion of the particle is given parametrically by #x(t)=3t^2-3#, #y(t)=2t^2# for t is greater than or equal to 0, how do you find the speed of the particle at t=1?
- For #f(t)= (lnt/e^t, e^t/t )# what is the distance between #f(1)# and #f(2)#?
- 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?
- Given Parametric equations: #x = 2(t)^2# and y = 4t how do you find the cartesian equation?
- For #f(t)= (sint,cos^2t/t)# what is the distance between #f(pi/4)# and #f(pi)#?