Question

112 PUINIS PREVIOUS ANSWERS SLALLE 15.2.07. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t. y = e-4, z = 5t - ; (0, 1, 0) (X(t), y(t), z(t)) =(

Answer 1

& not, yo é et 2-st - trg (0,1,0) find the value of t that creates the paint 20, 1.0) Substitute o for a : et=0 .00 check that t o work for the y and values - &- 460) 2 - 50 - 105 y=1 Z =0 These check to Find the tangent vector du dy = -4 é az 5-6+4 The tangent vector for all points to (t), is v (t) = {1} i + {-40 bj + {5-styk 14 ot d

we are interested in the tangent vector at the given kout J(t) = 1 3 - 4 84, +(5-5 (0)" }k 7 (t) = ; - Y; + Sk The vector equations of the tangent line is : (x, y, z) = (0,2,0) + s (i-4z +Sk) The parametric equations for this line are s o - 3 1 y = 1-us 2= 58