Elliptical cylinder surface area | Analytic geometryI have to find the equation of a Cylindrical surface area. This area has the generating lines parallel to the axis z. The directrix is an ellipse on the floor Oxy with center C(1;3;0) and vertices A(1;-1;0), B(-1;3;0).I tried to make a system with:- a = 2 // As the distance from the center and the B vertex is 2- changed X and Y values with those of the vertex A first- and then with those of the vertex B.I now have a system of 3 equations with variables a and b, but they're squared only, as they're supposed to be in an ellipse.I tried to solve it but it doesn't look good as the solution has parameters xand y not squared as well.Solution: 4 x 2 + y 2 − x − 6 y − 3 = 0

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Elliptical cylinder surface area | Analytic geometryI have to find the equation of a Cylindrical surface area. This area has the generating lines parallel to the axis z. The directrix is an ellipse on the floor Oxy with center C(1;3;0) and vertices A(1;-1;0), B(-1;3;0).I tried to make a system with:-   a  =  2 // As the distance from the center and the B vertex is 2- changed X and Y values with those of the vertex A first- and then with those of the vertex B.I now have a system of 3 equations with variables a and b, but they&#039;re squared only, as they&#039;re supposed to be in an ellipse.I tried to solve it but it doesn&#039;t look good as the solution has parameters xand y not squared as well.Solution:   4      x    2    +      y    2    −  x  −  6  y  −  3  =  0

hottchevymanzm · Accepted Answer

Explanation:- Asking you to find the equation of a surface in three dimensions is something of a red herring. Its generating lines are parallel to the z-axis and the directrix ellipse lies entirely in the x-y plane, so the equation of the elliptical cylinder will look exactly like the equation of the (two-dimensional) ellipse.- You’re on the right track by subtracting the center from the two vertices. You should find from this that the axes of the ellipse are parallel to the x- and y-axes, so in a coordinate system in which the ellipse is at the origin, its equation is   (      x    ′        /    a      )    2    +  (      y    ′        /    b      )    2    =  1.- To translate the center of the ellipse to a point   (      x    c    ,      y    c    ), make the substitutions       x    ′    →  x  −      x    c   and       y    ′    →  y  −      y    c   in the equation you derived for the ellipse centered at the origin.

Find the equation of a Cylindrical surface area. This area has the generating lines parallel to the axis z. The directrix is an ellipse on the floor Oxy with center C(1; 3; 0) and vertices A(1;-1;0), B(-1;3;0).

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