In Exercises 11 - 20, sketch the plane curve defined by the given parametric equations and find ai equation such that the parameter is eliminated, y = f(x) or x= g(y). 11. x =t and y = 3t
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- 11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t and Y=2tFind 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.Find a parametric curve that describes the intersection between the surface S: x2 + y2 - z2 = 0 and the plane P: z = x + 1.
- Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 3x2 + 2y2 + 6z2 = 29 at the point (−1, 1, 2).Exercises 15–17, find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. 15. Surfaces: x + y2 + 2z = 4, x = 1 Point: (1, 1, 1) 16. Surfaces: xyz = 1, x2 + 2y2 + 3z2 = 6 Point: (1, 1, 1) 17. Surfaces: x2 + 2y + 2z = 4, y = 1 Point: (1, 1, 1/2)Sketch the curve of the parametric equation. x=4sin t/2, y=4cos t/2.
- Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π by eliminating the parameter.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).Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?
- 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 parametric equations for the tangent line to the curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid 6x2 + 4y2 + 5z2 = 30 at the point (−1, 1, 2). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of the ellipsoid x2 + 2y2 + 2z2 = 4. Then find parametric equations for this curve. (x(t), y(t), z(t)) = for −1.1 ≤ t ≤ 1.1