Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point (2, 1, 2).

Q: Find the distance between the point (0,0,0) and the plane 2x – y + 2z = 4

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Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: 2)Passes point (1,3,7) and orthogonal to xy- plane.

A: The line which is orthogonal to x-y plane is lies on z-axis. Therefore the direction ratio's of the…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: How can we ensure that the decision boundary (separating hyperplane) of a perceptron does not always…

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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: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Find the distance from the point (3, -4, 2) to thea. xy-plane b. yz-plane c. xz-plane

A: The 3D view of the point is as below

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

Q: Find the standard equation of the sphere with the given characteristics. Center: (−4, 0, 0), tangent…

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Q: The line through the points (−3, 8,−4) and (1, 0, 8) intersects the yz-plane at _____.

A: We know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

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Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

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Q: find the distance from the point to the plane. (0, -1, 0), 2x + y + 2z = 4

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Find a parametrization of the curve. The vertical line passing through the point (3, 2, 0)

A: Consider the given point  3 , 2 , 0

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

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Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: Find a parametrization of the circle of radius 5 parallel to the yz-plane with center (-1, 4, 6).

A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: The distance between the point ( 9,8,3) and the plane x + y – 2z = 5 is .... %3D

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Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (8, 2, 0). (x, y, z) =…

A: Here we use partial derivatives to solve this problem.

Q: Find equations of two spheres that are centered at the ori- gin and are tangent to the sphere of…

A: Given radius=r=1 centered sphere at (3,-2,4) find the equations of sphere that are centered at…

Q: find a parametrization for the curve. the ray (half line) with initial point (2, 3) that passes…

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

Q: Find the point P nearest to Q = (−1, 3, −1) on the planex − 4z = 2

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Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the distance between the point (3, −2, 4) and the plane 2x − 5y + z = 10.

A: Given: The equation of a plane is 2x-5y+z=10. To determine: The distance between the point 3,-2,4…

Q: Find a parameterization for a circle of radius 4 with center (-4,4,-6) in a plane parallel to the yz…

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

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Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- vector space.

A: Query- Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3- D…

Q: Find the centroid (, ) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 19 120 y=

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Q: Classify the quadric surface. 9x2 + 3y2 − 6z2 = 54

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Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Is the point (-3, -4, 2) visible from the point (6, 7,0) if there is an opaque ball of radius 1…

A: Find the value of x, y and z. The value for the variables are  computed by using the midpoint…

Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

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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.