Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given y? by the equation x² = 1. 4

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

A:

Q: What is the differential equation of the family of ellipses with their centers origin and their…

A: Let us solve the problem using the basic equation of ellipse  later we will use different methods to…

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

A:

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point…

A:

Q: Find the minimum distance from the point (2, 4, 10) to the paraboloid given by the equation z = x +…

A:

Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

A:

Q: A particle follows the trajectory x(t) = 3 + 2t, y(t) = 10t – t2 with t measured in seconds and…

A: Given: xt=13t3+2tyt=10t-t2

Q: tind the point on the curve y=Jx that is closest to the point (3,0).

A:

Q: Q3 Find dyldx on the graph y secx + y = cos2x at point (1, 2).

A: We have to find the derivative of above function at (1,2) Please see the explanation below

Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

A:

Q: Find the tangent line. To the ellipse x²+4y²=8 parallel to the line x+2y=6

A: Equation of ellipse is , x2+4y2=8Differentiate w.r.t.x2x+8ydydx=0Subtract 2x from both…

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

A:

Q: Find the greatest and smallest values that the function f(x,y) = 4xy takes on the ellipse x +2y² = 1…

A: Let's find.

Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

A:

Q: A baseball is launched into the outfield on a parabolictrajectory given by y = 0.01x(200 - x). Find…

A: Given ------(1)   The average value of a functionon an interval is given by ------ (2) From the…

Q: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

A:

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the…

A: Given" Parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at…

Q: Minimum distance between the parabolas y² – 4x –8y + 40 = 0 and x² –8x –4y + 40 = 0 is (A) 0 (B) 3…

A:

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: 2 Find the point onthe curve y=Jx that is. the point (4,0). minimum distance from a

A:

Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

A:

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A:

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

A:

Q: The surface of a hill above the xy-plane is described implicitly by 3x² + y² + (z + 1)² = 2, z ≥ 0.…

A:

Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

A:

Q: Find the orthogonal trajectories of the family of parabola described by the equation (y – 3) = = cx…

A:

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

A:

Q: Find the minimum distance from the parabola: x - y2 = 0 to the point (0,3).

A: x - y2 = 0 x = y2  Let us take a point (x,y)=(y2, y) on the parabola

Q: Use Lagrange multipliers to find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme…

A: This question is related to Lagrange multipliers theorem. We will solve this question by using…

Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

A:

Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

A:

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Consider the equation хд,и — удуи — -и with the initial condition: u(x,y) : = 2 on the circle {(x,y)…

A: Given the equation as x∂xu-y∂yu=-u                  (1) write down the subsidiary equation of (1)…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

A:

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: Find the maximum and minimum valves of f(xy)=5x+Y on the ellipse X+36y=!

A:

Q: A water tank has the shape obtained by revolving the curve y = x^4/3 around the y-axis. What is the…

A:

Q: Find an equation of the parabola y = ax² + bx + c that passes through (0, 1) and is tangent to the…

A:

Q: Find the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

A: