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

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

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: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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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: Find the length of the curve 36y2 = (x — 4)3 , 2 ≤ y ≤ 3, y ≥ 0.

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Q: Find the minimum distance from the point (3, 0) to the circle x2 + y2 = 4.

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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 (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: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A: Let ax+by+cz+d=0 is a plane  Then distance from the  a point (xo,yo,zo) is D= |axo +byo +czo…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Evaluate the length of the curve x = 5 - y+1,0<y<3

A: Given, x=5-y+1 ,     0≤y≤3

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

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: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

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Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

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Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

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: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: Find the shortest distance from the point P(2,-1, 1) to the plane with =quation x - y + 2z = –1 and…

A: Shortest point of the given plane and point P.  Distance from the point P and Q

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: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4.

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Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: find the point p on the line y=5x that is closest to the point (78,0). what is the least distance…

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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: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

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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 slope of the tangent to the curve of intersection of the surface 3z=√36-9x²-4y² and the…

A: Consider the surface 3z=36-9x2-4y2and the plane x=1 at the point 1,-2,113.The objective is to find…

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: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

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

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Q: Find an equation of the tangent plane to the surface at the given point. 5x2 + 2y2 + 5z2 = 73,    P…

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Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

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

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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: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

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Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

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

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Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find