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- Find the parametric equations for the line through the point(0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1 − t, z = 2t, and intersects this line.11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t and Y=2tConsider the graph ofr(t) = 2t^2i + t^2j + t^3 kDetermine parametric equations of the tangent line to the curve at the point where the curve intersects the planex − 2y − z = 8.
- 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. x=e^t, y=e^(-2t)Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point ->(5,0,0). x=5e^t, y=te^4t,z=te^(t^5)4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line ⅓ (x – 4) = ½ (y) = z + 2.
- Find a parametric representation of the solution set of the linear equation.x + y + z = 1Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2) 2 ; y = 9t2-54. Determine the length of the parametric curve given by the following parametric equations. (a) x = t2 - 1, y = t3 + 1, 0 ≤ t ≤ 1 (b) x = cos(5t), y = sin(5t), 0 ≤ t ≤ π
- Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds to (-2, 0)Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces x2 + y2 + z2 = 14, x − y − z = 0, at the given point (3, 1, 2).Suppose a parametric equations for the line segment between (5,2) and (7,8) have the form: x(t)= a+bt y(t)= c+dt If the parametric curve starts at (5,2) when t=0 and ends at (7,8) at t=1, then find a,b,c, and d