Q5 Is it possible to construct a sphere that pass through the following points? (a) {(0,1, 2, ), (3,4, 5), (6,7,8), (9, 10, 11)} (b) {(0,1, –2), (1, 3, 1), (2, –1, 0), (3, 1, – 1)} If possible, find the equation of the spheres and hence reduce the equation in standard form. If not, explain the reason.

Q: Find an equation of the plane. the plane through the points (0, 5, 5), (5, 0, 5), and (5, 5, 0)

A: use the equation of plane(formula) for finding  the equation .

Q: Rhombus WXYZ with vertices W(1, 5), X(6, 3),Y(1, 1), and Z(-4, 3) in the x-axis W'

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Q: What is the center and radius of the sphere whose equation is (x + 1)2 + y2 + (z + 4)2 = 5? (-1, 0,…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Find an equation of the sphere with center (3,0,2) and passin Skecth the sphere. 10 -10 -10 -s 10 y…

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Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

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Q: 4. Using least square approximation, find the best line and parabola fitting to the points (i, Yi),…

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Q: a) Find the distance between the points (7,0,1) and (-5,4,2). b) Find the center and radius of the…

A: According to our guidelines we can answer only three subparts ,or first question and rest can be…

Q: Let P(-5, -3, -7) and Q(7, 11, 1) be two points in three dimensional space. Write an equation of the…

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Q: 5. Find the standard form equation of a sphere that has a diameter with endpoints (3, -2, 4) and (7,…

A: Given : The end points of a diameter of a sphere are  (3, -2, 4) and (7, 1, 4). To find : We have to…

Q: The equation represents Select one: x² + y² + z² + 6z = 4x + 12 a sphere with center(-2, 0, 3) and…

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

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Q: 18. Find the foci of the hyperbola. -号=1 * = 46 O (0, 7), (0, – 7) O (9, 0), (–9, 0) O (0, 9), (0, –…

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Q: 19. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) Answer + -4x + 3y + z = -14

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Q: Calculate the shortest distance between the point P = (3, 2, 2) and the plane 5x+y-2z = 3. (Do not…

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Q: Find an equation of the largest sphere with center (3, 2, 7) and is contained in the first octant.…

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Q: 3. Identify the vertex, axis of symmetry, and direction of the opening of the parabola y =x - 4x +…

A: Understand with help of graph

Q: Find the equation of- 1.1)a sphere 1.1.1) passing through (1,0,0), (0,2,0), (0,0,3) and (0,0,0)

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

Q: Find the equation of the sphere which passes through the origin and the points (0, 1. -1), (-1,2, 0)…

A: Use the genres equation of sphere passing through origin.

Q: Find an equation of a sphere if one of its diameters has endpoints (7,9, 9) and (3, 5, 7).

A: Given end points of diameterA=7,9,9 & B3,5,7

Q: Find an equation of the largest sphere contained in the cube determined by the planes x = 0, x = 8,…

A: given the planes:

Q: Find the equation of the sphere passing through P(- 4, 1, 4) and Q(6, - 3, 3) with its center at the…

A: Sphere equation

Q: 5/ Find the point at which the line through points P1(2. 3, 0) and P2 (-6. -3, 12) meets the plane…

A: Consider the points  P12,3,0 and P2−6,−3,12

Q: Find an equation of a sphere if one of its diameters has endpoints (7, 9, 9) and (3, 5, 7).

A: The endpoints of the sphere we have, (7,9,9) and (3,5,7)

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

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Q: Find the equation of the sphere if one of its diameters has endpoints (7, -2, 8) and (9, 2, 14)…

A: Given: The sphere diameters has endpoints (7,-2,8) and (9,2,14) which has been normalized so that…

Q: Find an equation of the plane. The plane through the points (4, 1, 4), (5, −8, 6), and (−4, −5, 1)

A: ivenThe plane through the points(4, 1, 4) , (5, -8, 6) and (-4, -5, 1)we have to find the equation…

Q: an equation for the plane consisting of all points that are equidistant from the points (-6, 4, 3)…

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Q: 2. What are the foci of this ellipse? 5 -5 O (-1, –4V5) and (–1, 4v5) O (-1, –2/5) and (-1,2/5) O…

A: By carefully examining the figure we will find that the major axis should pass through the line x =…

Q: B': 3. Trapezoid FGHI with verlices F(-5,-2), G(-2,-2), H(0, -6), and (-8,-6): y-axis F': H: G: I':

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

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Q: Z= (a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0, 0,…

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

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

A: The standard form of the equation of sphere is given by Where ( x0, y0, z0) is the center and r is…

Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the equation of the sphere if one of its diameters has endpoints (-5, -5, 1) and (-3, -1, 7)…

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Q: (-2,0,5) and (–1,2, 3). Find an equation of the sphere whose endpoints of a diameter are

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Q: What point on the parabola y = 3- x² is closest to the point (3,3)? The point on the parabola y = 3…

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Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. 9. 2. 25…

A: The vertex of ellipse x2a2+y2b2=1 is a point at which it makes its maximum turn.  Let a>b. Then…

Q: Find an equation for the sphere that has the points (8,2, –1) and (-4,–4,3) as endpoints on a…

A: Given points,

Q: 9. Find an equation of the parabola that satisfies the given condition: Vertex V(-1,0) and focus…

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Q: 3. 4. Circumscribing the triangle with vertices (a, U), (a, d), (U, %). 2a = 0. Ans. z2 + y+ ax- ay…

A: In the question we have to find equation of circle circumscribed in a triangle. NOTE - As per…

Q: Find an equation of the plane. The plane through the points (0, 2, 2), (2, 0, 2), and (2, 2, 0)

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Q: The points in a rectangular waterproofed room with dimensions 20 x 20 x 20 are given coordinates by…

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Q: 7. Rhombus FGHI with vertices F(6, -1). G(11, -3). H(13, -8). and (8. -6): scale factor = 2,…

A: Dilations involve multiplications. Scale factor 2 means every coordinate of original figure has to…

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: Find the equation of the plane passing through the points O = (0,0,0), A = (2,2, –4) and B = (-4,0,…

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Q: 15. In the xy-plane, (-3, 1) and (4, 3) are the endpoints of a diameter of a circle. What are the…

A: Endpoints of diameter are (-3, 1) and (4, 3).

Q: 5. The equation of the circle whose center is the centroid of the triangle with venices (-72 (4,-3)…

A: Formula to find coordinate of centroid is used when coordinate of all 3 vertices of triangle is…

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.