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b) (12,5 point) Find the equation of the cone surface whose directrix is the ellipse {4.x2...
3. a) (12,5 point) What is the definitions of cone and cylinder surfaces. Write the vectoral and parametric equations of them with their figures. b) (12,5 point) Identify and construct the surface whose equation is ra+yz = 0. Cone or cylinder surface.
Find the vertex, focus, and directrix of the parabola. 28y = x2 vertex (X,Y) = _______ focus (X,Y) = _______ directrix _______ Sketch its graph, showing the focus and the directrix.
9. (2 points) 4. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y 1 x2 9 y Oy2-36x x2 36 y Oy2 = -9x 5. Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7. (2 points) 1 x2 28 1 X = y2 28 -28y x2 Oy2 14x = 9. (2 points) 4. Find the...
Given the graph of the parabola below, with vertex at the origin and the point (4, 12) on the parabola, find the equation and directrix of the parabola. 18+ 16 14 (4, 12) 12 10- 1 8 6 4 2 - 4 -2 0 2. A) equation: y = -22, directrix: Y 1 B) equation: y = - 1x, directrix: y = 3 C) equation: y = x2, directrix: Y ساده Type here to search EI 6 2 2 -4...
Find the equation of the parabola with focus (10, -3) and directrix y = 3. Each equation below represents a conic section. Write the name of the corresponding type of conic. Explain how you know if it is a circle, ellipse hyperbola or parabola. a) 1 25 9 b) y2 + 6y + x - 6 = 0 c) x2 + y2 = 100
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi 1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find...
is Find an equation for, and identify, the surface that results when the surface x2 - y2 – 2z2 reflected about the plane Y = 2. b) Find an equation for, and identify, the surface that results when the surface x2 – 4y2 + x2 = ( is translated to the point D(2,-1,-4).
8. Find an equation for the ellipse whose graph is shown.9. Find an equation for the ellipse whose graph is shown.
Find the vertex, focus, and directrix of the following parabola. Graph the equation. y? - 2y +x=0 The vertex is (Type an ordered pair.) The focus is (Type an ordered pair.) The equation of the directrix is (Type an equation.) Use the graphing tool to graph the equation. Click to enlarge graph
Let S be the surface of the cone whose base is a disk of radius 2 in the plane z = 4 and whose vertex is at the origin (S includes the base of the cone, so that it is a closed, piecewise smooth surface), oriented outward. Let F(x, y, z) = (2x – cos(yz), 2y +exz®, sin(xy) – 42). Compute the surface integral ds. To recieve full credit, you must justify your work; in particular, if you are using...