Try to visualize the set of all points (x, y, z)in a coordinate space that are twice as far from the points Q(0, 3, 0) as from the point P(0, 0, 0) . Use the Distance Formula to show that the set is a sphere, and find its center and radius.

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 parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: 2. Find the distance of the point A : (1,0, 2) from the plane P: 3x +y+ z = 9.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

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

A: We have to use polar coordinates here.

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: Find the point on the plane x-y+z=7 that is closest to the point (2,4,6).

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Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y &lt; 3 , or within 3 units…

Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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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: Match the surfaces (a)-(e) with the contour diagrams (1)-(V, (M)

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Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

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: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

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: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Sketch the surface r = 2y? + 32².

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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 for the point P(x,y,z) on the plane 3x + y – z – 15 = 0 that is closest to the origin.

A: The distance of the point P(x,y,z) from the origin is: d2=x2+y2+z2 Now we have to minimize d if 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: 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: Let C be the intersection curve of the parabolic cylinder √2x2 = 2y and the surface 3z =√2xy. Find…

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

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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: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

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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: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: Show that the curve a(t) = (t, , ) lies in a plane and find the equation of this plane.

A: For all 't' , we have α'(t) = 1 , -1t2 ,-1 - 1t2α"(t) = 0 , 2t3 , 2t3 Now  α'(t) × α"(t) = 2t3 ,…

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

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Q: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

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 points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: Find an equation of the sphere containing all surface points P = (x, y, z)  such that the distance…

A: Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance…

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 b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

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

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

A: Topic = Sphere

Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

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Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are equidistant from the…

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Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: Let y ==a and z =. Find the intersection of these х x2 surfaces.

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Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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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.