Let (m, n)be the point at which a line is tangent to the ellipse + m = 1lf this line has x-intercept A = (a, 0and y-intercept B = (0, 6) what is the minimum value of ab?

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: To find the minimum distance from the given curve to the point using Lagrange multipliers method.…

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: If ƒx(a, b) = ƒy(a, b) = 0, does it follow that ƒ has a local maximum or local minimum at (a, b)?…

A: To determine: Whether the function f follows that it has a local maximum or local minimum at a point…

Q: Find the minimum distance from the point to the plane x - y + z = 3.

A: Now, formula of shortest distance of the plane ax+by+cz=d passing through the point (l, m, n) is,

Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

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Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

Q: The discriminant ƒxx ƒyy - ƒxy 2 is zero at the origin for each ofthe following functions, so the…

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Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

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Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point (a)…

A: Given: fx,y,z=xyz+3 Let fx,y,z=xyz+3 the level surface are given by, xyz+3=k        ,k∈ℝ…

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

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Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Use Lagrange multipliers to find the minimum distance from the plane x+y+z=5  to the point (5,4,4) .…

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Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Let L be the line with equation y = x – 1. Find the minimum distance between L and the point (4, 5)…

A: In order to use method of Lagrange multiplier, we first need to find the function to be minimized.…

Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: A bug crawls on the surface z = x2 - y2 directly above a path in the xy-plane given by x = ƒ(t) and…

A: We are given that the bug crawls on the surface z = x2 - y2 and x = ƒ(t) and y = g(t).  So,…

Q: ) Prove that the Point P(!,-) is a minimum Point of the curve y =lnx

A: Any point (x,y) is minimum for a given curve if it satisfies below two condition, a) First…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Given surface plane: x+y+z=1 Point (8,1,1).

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

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Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Find the minimum distance from the point (6, 0, 5) to the plane x - y + z = 3. (Hint: To simplify…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Given y=x3+cx2+d

Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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

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Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

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Q: Suppose that f(x, y) = x' + y – 2xy Then the minimum is

A: Solution is given below:

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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Q: Suppose that f(x, y) = x* + y* – 2xy Then the minimum is

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

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