(a) ) Find an equation of the sphere that passes through the point (1, -2,0) and centered at the point (2, -1, 3). (b) Show that the following equation

Q: hyperbola, vertices (±3, 0), foci (±6, 0)

A: Equation of hyperbola :x2a2 - y2b2 =1 , when vertices is on the x-axis.

Q: Determine a cartesian equation of the plane through the points  P1 =(1,2,-1), P2=(0,2,-3) and…

A: Determine a cartesian equation of the plane through the points  P1 (1,2,-1), P2(0,2,-3) and parallel…

Q: 3. The plane in ' with equation 4x=34 %3D

A:

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A:

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of diameter ::

Q: Find a set of parametric equations for the parabola whose equation is y = 9 - x2.

A: Given equation is, y=9-x2

Q: Explain why it is not possible for a hyperbola to have foci at (0, -2) and (0, 2) and vertices at…

A: The standard form of the equation of a hyperbola with center (0,0) and transverse axis on the y-axis…

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given that End points of diameter (2,9,13),(2,-7,-6)

Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x - 5y…

A:

Q: Find an equation of the sphere that passes through the point (6, –2, 3) and has center (-1, 2, 1).

A:

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Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: Find an equation of the plane through the given point and parallel to the given plane. origin 2x -…

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Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

A:

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(-1,…

A: Equation of sphere  standard form of sphere equation

Q: Find the Cartesian equation of the plane containing the points A(- 1,0, 1), B(2, 1, 3), C(4, – 2,…

A: topic - equation of plane through three points

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

A:

Q: Find the parametric, vector and Cartesian equations of the Ellipse with vertices (1.7, 2.9) and…

A:

Q: Determine the equation of the plane that contains the points P_0 = (1, 0, 0), P_1 = (0, 1, 0) and…

A:

Q: Find an equation for the conic that satisfies the given conditions. parabola, vertical axis, passing…

A: A parabola with vertices passing through 0,5,1,4, and -2,-5. Find the equation for the conic that…

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

A:

Q: Find an equation of the sphere with center What is the intersection of this sphere with

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Q: Use a translation of axes to put the conic in standard position. Identify the graph, give its…

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Q: Find an equation of the plane indicated in the figure. Equation:

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Q: Find parametric equations for the line containing the points P(0,2,0) and Q(1,3,5).

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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Q: Find an equation of the plane. The plane through the point (9, -1, -7) and parallel to the plane 7x…

A: Answer

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 equation of plane with vertices P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A: We have to find

Q: (-3,3) 7 6 5 4 + لا 3 2 (-3,2) 1 -6 -5 -4 -3 -2 -1₁ -2 -3 -4 -5 -6 -7 1 2 3 4 5 6 7

A:

Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

A:

Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: Find an equation of the sphere with center (-3, 2,5) and radius 4. What is the intersection of this…

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Q: Find an equation for the plane through the points (-2, –2, 0),(-1,4,–9), and (–10, –6, –4). tion for…

A: Given points are -2,-2,0 -1,4,-9 and -10,-6,-4find the equation of a plane

Q: Find an equation of the sphere that passes through the point (7, 5, -3) and has center (5, 8, 1).

A:

Q: 6. Find an equation of the sphere that passes through the origin and whose center is (3, 1, 3).

A:

Q: Find an equation of the plane that contains all the points that are equidistant from the given…

A: Let plane contain point x,y,z.

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

A:

Q: What are the intersections of the conic section formed by the points A(0,1),B(2,3),C(5,4),D(1,…

A: Below are graph and input view.

Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

A:

Q: find the standard equation of the sphere with center (4,3,3) and radius 7

A:

Q: Find a set of parametric equations for the parabola whose equation is y = x2 - 25.

A: We have to find a set of the parametric equation for the given parabola    y=x2-25   Consider the…

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

Q: Find the standard equation of the sphere with center (-2, 5, -3), and radius 5.

A:

Q: The signal received by a parabolic antenna is concentrated in its receiver, which is placed,…

A: For the Paraboloid,z-axis is it's Principal Axis,Also, it is symmetric with the lines x = 0 (yz…

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(−1,…

A: Given, Centre =C(-1,5,4) And Radius , R=4

Q: Find an equation of the sphere with center (-4, 2, 8) and radius What is the intersection of this…

A: Given centre -4,2,8 and radius 5 of the sphere .The equation of a sphere is given by the…

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.