Find the point on the sphere (x - 1)² +y² + (z + 9)² = 9 nearest to a. the xy-plane. b. the point (6,0, – 9).

Q: find the center and the radius of the sphere x^2+y^2+z^2+2x-5z=0

A: Equation of the sphere is  (x-a)² + ( y-b)2+ (z-c)2 = r2  Where (a,b,c) are the centre and r be the…

Q: find the center and radius of the sphere x^2+y^2+z^2+8x-8y+6z=-16

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Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Find the center and radius of the sphere X² + y² + z² −2x−4y + 8z + 17 = 0

A: Given: Equation of a sphere is x2+y2+z2-2x-4y+8z+17=0. To find the center and radius of the sphere.…

Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = sqrt(x2 + y2).

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Q: close

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Q: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

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Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

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Q: Q3: Find the points on the surface x^2+z^2-6=0, closest to the origin.

A: The distance of the point on the surface is given by d=x2+y2+z2. To obtain the distance insert the…

Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

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Q: Find an equation of the largest sphere that passes through the point (-1, 1,4) and is such that each…

A: Find the equation of sphere.

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 10, 5). O A.…

A: To find:-   Equation of the sphere that passes through the origin and whose center is (-10, 10, 5).

Q: Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

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

A: Solution is given below:

Q: Find the center and radius of the sphere: x^2+y^2+z^2-8x+2y+4z-9=0

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Q: Find the center C and the radius r of the sphere S: x2 + y? +z2 + 4x + 8y- 8z =-11

A: General equation of sphere  (x-h)2+(y-k)2+(z-p)2 = r2  center (h,k,p)  radius = r

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: The equation of the sphere with center (4,-2, 9) that touches that -axis is OA. (x – 4)* + (y + 2)*…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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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 following sphere: x2 + 2x + y? + z2 + 4z + 1 = 5

A: The equation of the sphere is x2+2x+y2+z2+4z+1=5 To find its center and radius.

Q: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: Q3: Find the points on the surface x^2+z^2-25=0, closest to the origin.

A: Distance formula is d2=x2+y2+z2 .......(1) From the given equation z2=25-x2 ....... (2)

Q: (b) Find the points where the line passing through (-2,0,1) and (-4,1,4) intersect the sphere x2 +…

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Q: Q3) Find the centers and radius of the spheres in x? + y? + z? + 4x - 4z = 0 x? + y? + z? - 6y + 8z…

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Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Which of the following point is the closest point on the sphere z² + y² + z² = 4 from the point…

A: Given Equation of Sphere X2+y2+z2=4 And point (3, 1, -1)

Q: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

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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 point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200…

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Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 6y + 8z = 0

A: To Determine: Find the center C and the radius a for the spheres  Given: we have an equation…

Q: Find the extreme values of the function ƒ(x, y, z) = xy + z2 on the circle in which the plane y - x…

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Q: The equation of the sphere with center (5,-8, 4) that touches that y-axis is OA. (x – 5)² + (y + 8)*…

A: To find the equation of a sphere with center (5,-8,4) that touches the y-axis.

Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

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Q: Find the point on the sphere x^2 + y^2 + z^2 = 8 that is closest to the point P(2, 1, 1)

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Q: Find the largest and smallest distances between the point P(1, 1, 1) and the sphere x² + y? + z? –…

A: Given circle is x2+y2+z2-2y+6z-6=0, and P(1, 1, 1) Let C be the center of the circle.…

Q: The sphere, x + y² + z? – 4y + 2z – 20 = 0, has a center at which point? (0,-2,-1) (0,2,-1) (2,1,1)…

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Q: Find the radius and center of the sphere. x2 + y² +z² - 6x + 8y – 4z = - 13 r=

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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: Find the center and radius of the sphere x2 + 18x + y? + 4y + z2 + 10z = –74 Center: ( || ) Radius:

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Q: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: Find the center and radius of the sphere x? - 16x – 7+y? + 10y + z² – 4z = 0 OA C(8,- 5,2), r = 10 O…

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Q: 9. Find the center and radius of the sphere given by 3x + 3y? + 3z2 = 10 + 6y + 12z.

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Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: D is the region enclosed by the parabolas z = y²-9 and 2 - y² +9.

A: Let, I=∫∫Dx+y+2dA x=y2-9 and x=-y2+9 Power rule for the integration: ∫xndx=xn+1n+1+C ∫cdx=c∫x0dx=cx

Q: Find the point on the sphere X+y+=4 and the point on The sphere x+y ansi- 2 Selution:-

A: To find the point on the sphere which is farthest from the given  point (1,-1,1).

Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: Find an equation of the sphere that passes through the origin and whose center is (6, – 6, 3). OA.…

A: We will find the equation of sphere as following.

Q: Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point…

A: Given sphere, x2+y2+z2=1 Consider gx,y,z=x2+y2+z2-1=0 The square of the distance between the points…