The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

Q: Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are…

A: Sphere equation x-42+y-52+z-22=16

Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

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Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…

A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…

Q: Sketch the surfaces ASSORTED 4y2 + z2 - 4x2 = 4

A: Given:  And can be written as,  Therefore, The obtained function is in the form of Hyperboloid…

Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

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Q: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: Find a Cartesian equation for theplane tangent to the hyperboloid x2 + y2 - z2 = 25 at the point(x0,…

A: If a hyperboloid is defined as f(x,y,z)=0, then the tangent plane at the point (a, b, c) is:…

Q: Find the point on the sphere  x2+y2+z2=900 that is farthest from the point (−19,−8,11).

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Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y + = 3 and the paraboloidz =…

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Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

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Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

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Q: Find the equations of the sphere through the circle x + y +2 =1, 2x+ 4y+5z= 6 and touches the plane…

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Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Find the center and the radius of the sphere. x2+y2+z2+3x+3z=

A: See the details solution in below

Q: Find the center and radius of the sphere. * + + 5z +x+y+z= 4 5x +

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Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Find the equation of the sphere with center at (-3, 2, 4)and of radius 6. A (x-3)2+ (y – 2) ²+ (z-…

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Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

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Q: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

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Q: Determine the center of the sphere x2+y2+z2+8x+6y+10z=0.

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Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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Q: The equation of the sphere with center (9,-6, 10) that touches that -axis is OA (x - 9)? + (y +6)* +…

A: The general equation of the sphere with center (a, b, c) is given by (x-a)2 + (y-b)2 + (z-c)2 = r2…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: Find the point on the sphere x²+y2+z²=1225 that is farthest from the point (6,9,24).

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Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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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: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: Classify the quadric surface ² - y² - x² + 4x = 5. 2 य

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Q: The equation of the sphere with center (3,-10, 9) that touches that y-axis is OA. (r-3)2+ (y 10)+…

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

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Q: The equation of the sphere with center (7,-3, 1) that touches that y-axis is OA. :-7° + (y +3)* +…

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Q: Sketch the section of the surface at y 0. -6 -4 -2 6. -2 2 -6 -4 -6 -4 -2 -6 -4

A: The objective of the question is sketch the section of the surface at y=0.

Q: 4x? + у? - 327 25 3z2 = 25

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Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

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 point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

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Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

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Q: Let 11 be the surface with the equation = 2√y+1 and let 12 be the sphere with equation x²+y+z² 16x +…

A: Given data÷ Find the center and radius of the sphere   x2+y2+z2-16x+16y-4z+76=0   General form of…

Q: Find an equation for the sphere with the given center and radius. Center (0, -4, -1), radius 9 O x2…

A: In this question we have to find the equation of sphere.