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

Q: Explain why the curve of intersection of the surfaces x + 3y? – 2z2 + 2y = 4 and 2x? + 6y? – 4z2 –…

A:

Q: Sketch the surface..........CYLINDERS.............x2 + 4z2 = 16

A: Here we have to draw the surface of cylinder having equation  x2+4z2=16

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: Determine the point on the plane 4x- 2y + : = 1 that is closest to the point (-2,-1,5)

A:

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

Q: Solve for the distance from the point (-5, 4, 5) to the plane −x+4y−5z=4.

A: Given Plane: -x+4y-5z=4 and Point: (-5,4,5)

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

A:

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

A:

Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

A:

Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

A:

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

A:

Q: What is the shortest distance from the surface ry + 15x + z2 = 204 to the origin? distance =…

A:

Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

A:

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

A:

Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

A: The given surfaces are sketched using online 3D calculator.

Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

A:

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

A:

Q: Find an equation of the sphere with center (2,-3,6) that touches the xy-plane.

A:

Q: Write the equation of the sphere centered at (5, – 2, 4) with radius 3.

A:

Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

A:

Q: Sketch the surfaces ASSORTED 16x2 + 4y2 = 1

A: we have to sketch the the surface 16x2+4y2=1

Q: Find the distance from the point to the plane (2,-3,4) , x+2 y - 2 z = 13

A:

Q: find the distance from the point to the plane. (6, 0, -6), x - y = 4

A: x1,y1z1=6,0,-6…

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

A:

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

A:

Q: Find the equation of the sphere which passes through (2, 1, 3), (3, 2, 1), (1, –2, –3), (–1,1, 2).

A: Given that the sphere passes through the points (2,1,3), (3,2,1), (1,-2,-3), (-1,1,2).

Q: Find the coordinates of the point located in the xy-plane, four units to the right of the xz-plane,…

A: Let the coordinate of the point located in the xy-plane is x,y,0

Q: Find an equation of the sphere concentric with the sphere x^2 + y^2 + z^2 + 4x + 2y − 6z + 10 = 0…

A: Topic = Geometry

Q: Find the point P on the line y=6x that is closest to the point (74,0).  Type an ordered pair.

A: Given:The line y = 6x and a point (74,0).Let p be the point that is closest to the point (74,0). Let…

Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

A:

Q: Determine the distance from point Q = (2, 6, 9) to the plane x + 2y + 2z = 8

A:

Q: Determine the center and radius of the sphere 2x2+2y2+2z2-12x-24y-36z=0

A: We have to find center and radius

Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

A:

Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

A:

Q: What is the shortest distance from the surface xy + 6x + z² = 48 to the origin? distance =|

A:

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

A:

Q: What is the y-coordinate of all points in the xz-plane?

A: Plane: The y-coordinate of all points in the xz plane , i.e. we need to put y=0.

Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

A:

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: Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

A: Solution:- We have to  Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Q: Find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5 Thank you.

A: To find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5

Q: Find the distance from the point (3, -4, 2) to the xy-plane

A: Given: 3,-4,2

Q: Find the distance from the point (-4,3,-2) to the yz-plane.

A: