Find the values a and b such that the cone ax² + by² + z² = 0 and the ellipsoid 2.x2 + 4y? + z² = 42 intersect and are perpendicular to each other at the point (1, 3, 2).

Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: A point moves along the intersection of the elliptic paraboloid z = 10x + 11y and the plane y = 1.…

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Q: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

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

A: Given,

Q: to Find lagrange Muitiplier use point P (x 191Z) closest to the origion 2x +y -Z=5 .veriky .verily…

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Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

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Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: Solve Sff, 3x² + 3y²dV by using cylindrical coordinates, where G is a solid in the first octant that…

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Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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

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Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

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Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Modify the given figure as shown in Figure 1.

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

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Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: Find the surface area of the cone frustum generated by revolving the line segment y-/2) + (1/2, 1…

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Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

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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: Find a point on the ellipsoid x2 + 4y2 + z2 = 9 where the tangent plane is perpendicular to the line…

A: Given  The equation of ellipsoid is given by fx,y,z=x2+4y2+z2-9 The line is x=2-4t, y=1+8t and…

Q: 28. Show that the ellipsoid 2x² + 3y² + z² = 9 and the sphere %3D x? + y? + z? - 6x – 8y – 8z + 24 =…

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Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Find all planes which (i) are tangent to the elliptic paraboloid z = x² + y², and (ii) pass through…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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Q: A point moves along the intersection of the elliptic paraboloid z = 6r + 7y and the plane y = 2. At…

A: Given: A point moves along the intersection of the elliptic paraboloid z = 6x2 + 7y2 and the plane y…

Q: Find the points on the cone z = x + y2 that are closest to the point (8, 2, 0). %3D (x, y, z) =…

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

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

A: Given equation of the cylinder is  y2=4ax, say φ1=y2-4ax=0 and the general equation of the ellipsoid…

Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: Line integrals

Q: Find the point closest to the origin on the curve of intersection of the plane 2y + 4z = 5 and the…

A: We have to find the point closest to the origin on the curve of the intersection of the plane…

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

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Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

Q: Find a parametrization for the line segment joining points (0, 2) and (4, 0) using the angle 0 in…

A: Given: The line segment joining (0, 2) and (4, 0). Do the construction as in below figure