Find the orthogonal trajectories of family of hyperbola with center at the original and the length of semi-minor axis as 2.

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

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Q: Find the distance from the point (-5, -1, -3) to the plane 5x + 3y + 2z = 1

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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 a parametrization for the curve. the line segment with endpoints (-1, 3) and (3, -2)

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,4) and…

A: Given,  A line segment with endpoints 4, 4  and  6, 1  We have to find the parametrization of the…

Q: Show that the parabola y = ax2, a ≠ 0, has its largest curvature at its vertex and has no minimum…

A: Using the relation,

Q: How can we ensure that the decision boundary (separating hyperplane) of a perceptron does not always…

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Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

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Q: Find the distance between the point (3,4,5) and the plane 2x + 4y 3z = 12.

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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 the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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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: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

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

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

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: A suspension bridge with weight uniformly distributed along its length has twin towers that extend…

A: The general equation for a parabola is given as, y=kx2 Let the x-axis represents the road surface…

Q: 4 Find a parametrization for the line segment with endpoints (-1,3) and (3,-2).

A: 4) To find the parametric equation of line segment with endpoints (-1,3) & (3,-2)

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

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Q: Find the orthogonal trajectories of the family of circles with center at the point (0, 1) and radius…

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Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: Find the distance from the point (-3, 4, -1) to the plane 5x−4y−5z=−3.

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Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

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Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: Find an equation of the sphere with center (2,-3,6) that touches the xy-plane.

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Q: Derive the orthogonal trajectories of the family of hyperbolas ??=?.

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

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Q: Find a parametrization for the line segment beginning at P, (-5, - 2,3) and ending at P2 0, 5/4

A: We have to use parameterization of the line.

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

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: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…

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Q: Find the distance between the point (3, −2, 4) and the plane 2x − 5y + z = 10.

A: Given: The equation of a plane is 2x-5y+z=10. To determine: The distance between the point 3,-2,4…

Q: Show that the parabola y = ax2, a  0, has its largest curvature at its vertex and has no minimum…

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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: The curve y = (64x – 4x³ )m bounds the shaded section on top and the x-axis on the bottom. Determine…

A: Given curve, y=64x-4x3 The shaded region is shown as: Formula for the centroid x, y in a region is…

Q: Find the gardientoff at the indicatedpoint. %3D

A: Given,

Q: Find a parametrization for the ray (half line) with initial point (-4,3) that passes through the…

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

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Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: A suspension bridge with weight uniformily distributed along its length has twin towers that extend…

A:

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

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Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

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