Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 10 along the x-axis, minor diameter 6 along the y-axis, and is oriented counter-clockwise. Your parametrization should make the point (5,0) correspond to t=0. Use tt as the parameter for all of your answers. x(t)= y(t)=

Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter 10 along the x-axis, minor diameter 6 along the y-axis, and is oriented counter-clockwise. Your parametrization should make the point (5,0) correspond to t=0. Use tt as the parameter for all of your answers. x(t)= y(t)=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

See similar textbooks

Similar questions

Consider the ellipse E in the xy-plane defined by the equation ax2 + y2 = 1 where a is positive. (1) Find a parametrization r(t) of E (2) Find all the points where r(t) is orthogonal to r'(t).
Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line with parametric equations x = 2 − 4t, y = 1 + 8t, and z = 3 − 2t
Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V , and rotated along the y-axis with constant angular speed ω. This makes the liquid rotate, and eventually at the same angular speed as the container. The surface of the liquid becomes convex as the centrifugal force on the liquid increases with the distance from the axis of the container. The surface of the liquid is a paraboloid of revolution generated by rotating the parabola y = h + ω2x2/2g around the y-axis, where g is gravitational acceleration and h is shown below. (You can take g=32ft/s2 or 9.8m/s2). Express h as a function of ω. (2) At what angular speed ω will the surface of the liquid touch the bottom? At what speed will it spill over the top? (3) Suppose the radius of the container is 2 ft, the height is 7 ft, and the container and liquid are rotating at the same constant angular speed ω. The surface of the liquid is 5 ft below the top of the tank at the central…
find a parametrization for the curve. the left half of the parabola y = x^2 + 2x
find a parametrization for the curve. the lower half of the parabola x - 1 = y2
find a parametrization c(t) of the curve satisfying the given condition. y = 3x − 4, c(0) = (2, 2)
Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.
Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to two decimal places.
Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.
find a parametrization c(t) of the curve satisfying the given condition. y = x2, c(0) = (3, 9)
Find a parametrization of the circle of radius 6 in the xy-plane, centered at the origin, oriented clockwise. The point (6,0) should correspond to t=0. Use t as the parameter for all of your answers. x(t)= y(t)=
Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0 corresponds to (0, 0)