determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

Q: Obtain all the umbilical point of the Hyperboloid of two sheets {x^2+y^2-z^2=1}.

A: consider the equation {x2+y2-z2=1}

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: 5- 4- Find the volume of the solid created by rotating the following curve y = 3vx about the y-axis.…

A:

Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: Find the uolume of the soild olbtained by the grophs bounded by potaling the begion Y = x² +1 and Y…

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: Find the center of mass of a thin plateof density δ = 3 bounded by the lines x = 0, y = x, and the…

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Q: 7x + 8y2 and the planex = 3. At what rate is z changing with A point moves along the intersection of…

A:

Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: Given∫03∫09-x2∫3--x2-y2x2+y2 dz dy dxTo convert it into polar coordinateswe know thatx=rcosθ,y=rsinθ…

Q: find a parametrization for the curve. the ray (half line) with initial point (-1, 2) that passes…

A:

Q: A thin plate of constant density k, bounded by the parabola y=3x² and the line y=3 has a mass 4k.…

A: If mass of a region R bounded between y=f(x) and y=g(x) from x=a  to x=b  Then there two moments,…

Q: Determine the centroid formed by revolving about the y-axis, the a bounded by the curve y = x*, the…

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Q: find the centroid of the solid formed by revolving about the x-axis the solid formed by the curve…

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Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by…

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: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

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Q: Find the centroid of the region between the semicircle y = v1 – x2 and the top half of the ellipse y…

A:

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: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

A:

Q: A point moves along the intersection of the elliptic paraboloid z = 3x² + 5y² and the plane y = 4.…

A: We are given the curve Z=3x2+5y2 and y=4   Now we know that the rate of change is simply derivative…

Q: Point W is the centroid of triangle TRV. VX = 204 and RW = 104. The length of RY = ____.

A: We have the given triangle as It is given that Point W is the centroid of triangle TRV. VX = 204 RW…

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A: Given,

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

A:

Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find the centroid of the region bounded by the given curves. y = 8 sin(5x), у 38 cos(5x), х-D0, х 3…

A:

Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

A:

Q: The ellipsoid 4x² +2y² + z² arametric equations for the tangent. line to this ellipse at th = 16…

A: The given equation of ellipsoid is 4x2+2y2+z2=16 intersects the plane y=2 in an ellipse. Let…

Q: Find the curved surface area of the solid generated by revolving the part of the curve y=x² from…

A: Given curve is                                               y=x2 from     (0, 0) to (6, 6) Rotation…

Q: Maximize xyz on the ellipsoid

A: See the details solution in below

Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

A:

Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

A:

Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: Find the centroid (¯x,¯y) of the triangle with vertices at (0,0)(1,0) and (0,5) x¯=    y¯=

A: Answer is given in next step.

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

A:

Q: .Estimate vu in cylindrical form, in the orthogonal curvilinear coordinates

A: Given: We consider elliptic in cylindrical form .

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

A:

Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…

Q: Q1,- A- Locate the centroid (X only) of the shaded area y=12-3x Fig.L.A

A: X= My/M  Y= Mx/M  X,Y are coordinate of centroid.

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: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

A:

Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…

A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…