Find the point lying on the intersection of the plane x + y + 4 z = 0 and the sphere x2 + y2 + z2 = 25 with the largest z-coordinate. 4V17 13V17 + 2 16 V17, 221 (х, у, 2) %3D 221 51

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 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: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: parametrizes the portion of the sphere x² + y² + z² = 9 that is above the xy-plane and below the…

A:

Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

A:

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

A: We have given the equation This is a sphere of radius 2, and with a center at (5, 5, 2).

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

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

Q: Evaluate (x2 + y? + z)dS, where S is the portion of the plane z = x + 2 that lies inside the…

A:

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: close

A:

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

A:

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ &amp; y=rsinθ. The…

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: Evaluate x² zdS, where S is the part of the plane z = 2 + 3x + y above the rectangle [0, 2] × [0, 5]

A:

Q: Find the equations of planes that just touch the sphere (r- 1)² + (y– 5)² + (z - 4)² = 25 and are…

A: Given : Equation of sphere (x - 1)² + (y - 5)² + (z - 4)² = 25

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

A:

Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

Q: Find the area of the part of the sphere x2 + y2 + z2 = 100z that lies inside the paraboloid z = x2 +…

A:

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: Enclosed by the paraboloid z = x² + 3y? and the planes x = 0, y = 1, y = x, z = 0

A: We know that, volume under surface z=fx,y and above the region D in xy-plane is given as…

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 11, – 2).…

A: Given: Origin point : ( 0 , 0 , 0 ) Center : ( -10 , 11 , -2 )

Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 4x + 6y - 10z = 11

A:

Q: The portion of the sphere x² + y² + z² = 25 inside the cylinder x2 + y² = 9

A: Given: The portion of the sphere x2+y2+z2=25inside the cylinder x2+y2=9 To find the area of the…

Q: The solid that is the common interior below the sphere x + y + z = 80 and above the paraboloid z =…

A: We need to find the upper limit for the given integral.region is bounded below by the sphere and…

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

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

A:

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

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

A:

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

A:

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

A:

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

A:

Q: Find the center C and the radius r of the sphere S: x2 + y2 + z2 + 4x + 8y – 8z =-11

A: A geometrical object which is in the shape of ball is called sphere. Outer surface of sphere is…

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)…

A:

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

A:

Q: b) Find the center and radius of the sphere x+y+z6x+4y-10z+25%=D0. C) Compute a ·b, axb, and…

A:

Q: Use Lagrange multipliers to find the maximum and minimum of f(r, y, z) = -r + 2y + 2z on the ellipse…

A:

Q: he cylinder x² + y² = 2y and the plane

A: Shift cylinder at origine as centre

Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

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

A:

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0. %3D

A: Distance between parallel planes d=(d2-d1) /(sqrt(a2+b2+c2)

Q: Find an equation for the sphere centered at (1, -2, 3) containing the origin. V14 = x + y+ z 14 = x?…

A:

Q: Find the equations of planes that just touch the sphere (x−5)^2+(y−3)^2+(z−1)^2=9 and are parallel…

A: Solution  Given (x−5)^2+(y−3)^2+(z−1)^2=9 (a)  Parallel to the  xy-plane:   ( z-1)2= 9   z - 1= | 3…

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 area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the center and the radius of the sphere. x^2+y^2+z^2-6x+3z=0

A:

Q: Find the center and radius of the sphere x2 – 12x – 4 +y? + 4y + z? – 20z = 0 ОА С (6, - 2,10), r…

A:

Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

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…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.