Find the maximum and minimum values of f(x, y) = 2r + y on the ellipse r? + 25y = 1 %3D %3D maximum value: minimum value:
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- Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse x2/a2+y2/b2=1.about x-axis.given that a2-b2=1?Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to two decimal places.
- Find the points on the curve of intersection of the ellipsoid x²+4y²+4z²=4 and the plane x-4y-z=0 that are closest to the origin and find the minimum distance.Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the parabola x = 4y2 if d(x, y) = 5x kg/m2.Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2. Calculate the slope of the resulting ellipse at the point (2,1,2).
- The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. Find the points on the ellipse that lie closest to and farthest from the origin.(a) Where does the normal line to the ellipse x2- x y + y 2 = 3 at the point (1, -1) intersect the ellipse a second time?Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem using lagrange