Find an equation of the largest sphere with center (3, 2, 7) and is contained in the first octant. Be sure that your formula is monic. Equation: = 0

Q: Find an equation of the sphere that passes through the origin and whose center is (3, 1, 4).

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Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

Q: Find the center and radius of a sphere with the equation: 8x + 4z = 1 − 2x^2 + 20y − 2y^2 − 2z^2.

A: Given the equation of the sphere 8x+4z=1-2x2+20y-2y2-2z2

Q: Identify the quadric surface each of the following equations represent and sketch its graph. O 92" +…

A: 9 x2 + 4y2 + 36 z2 = 369 x236+4 y236+36 z236=1x24+y29+z21=1x222+y232+z212=1

Q: 5. Show that the equation represents a sphere, and find its center and radius: x²+y? + z2 – 8x – 10y…

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Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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

A: Equation of the sphere

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

A: Given endpoints of diameter ::

Q: Find the coordinates of the foci for the following hyperbola. (x – 1)? (y + 1)? 1 64 16

A: I am going to solve the given problem by comparing it with the standard form of hyperbola whose…

Q: Find center, foci , vertices, asymptotes and radious of 2x? + 2y² – 28x + 12y + 114 = 0

A: Given: 2x2+2y2-28x+12y+114 = 0

Q: Determine the center-radius Form of the equation of the sphere who diameter has endpoints at (2, -3,…

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

Q: Find an equation of the largest sphere with center (6, 2, 8) that is contained in the first octant.…

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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: Complete the square to write the following equation as standard equation of a sphere and find center…

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Q: A conic section is said to be circle if the eccentricity e = 1. Select one: O True O False

A: The eccentricity of a conic section is a non-negative real number that uniquely characterizes its…

Q: Find the center and the radius of the sphere. x2 +y? +z? +5x + 6z = 0

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Q: Find the center and the radius of the sphere. x2+y2+z2+4x-5z=0

A: Comparing with standard equations of sphere,

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

A: Solution: The objective is to find the standard equation of the sphere

Q: Find the vertex, force, and directrix of the parabola x^2=7y

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Q: By differentiating implicitly, find the slope of the hyperboloid x² + y? – 22 =1 in the x-direction…

A: Given that: x2+y2-z2=1

Q: In each part, find the standard equation of the sphere that satisfies the stated conditions. (a)…

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Q: c) Find the center and radius of the sphere whose equation is

A: Given, we need to evaluate the norm of the following vectors. i=<-1,2,4>ii=-i+7j

Q: Find an equation of a sphere if one of its diameters has endpoints (5, 0, 6) and (7, 4, 8).

A: Solution of the problem as follows

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

A: Use standard equation of sphere

Q: A. Given the following information about the hyperbola, find i. FOCI: (-4, 0) (4, 0); VERTICES:…

A: # we are entitled to solve one question at a time , please resubmit the other if you wish to get it…

Q: Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

A: I have appended the formula used in the solution part.

Q: a) [. Show that the equation 6x + 6y6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Given the points P=(1,0,1) and Q=(5,-4,3) find an equation for the sphere for which the segment PQ…

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

A: To find the standard equation of sphere.

Q: Complete the square to write the equation of the sphere in standard form. Find the center and…

A: 9x2 + 9y2 + 9z2 − 6x + 18y + 1 = 0

Q: a) [ Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: Find the surface of the regular pyramid.

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Q: The three-dimensional quadric figure below is described by: x² + 2y? + 2z – 5 = 0

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Q: Find an equation for the sphere with a) center at the origin and radius length r = b) center (2, –…

A: Let the coordinates of centre of sphere be a, b, c and radius be r.

Q: Which quadric surface is this? *- ² + = 1 | Hyperboloid of One Sheet Hvnorholeid of Two Shoots

A: We are asked to identify the quadratic surface,

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: Find the equation of the sphere

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Q: Determine the equation for the sphere whose center and radius are given. Center Radius V13 (1,3,1)

A: Let center h,k,l=1,3,1 and radius r. Equation of the sphere with center h,k,l and radius r is given…

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: Using the property of Re z and Im z to show that the hyperbola x2- y2 = 1 can be written as: z? +…

A: We know that x=Re(z)=z+z2 and y=Im(z)=z-z2i. We are given the equation of hyperbola x2-y2=1.

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A:

Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

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Q: a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find…

A:

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y2 1 can be written as: z? +…

A: See the attachment

Q: The length of the latus rectum of a hyperbo is equal to 18 and the distance between the foci is 12.…

A: Here, given that the conjugate axis is parallel to the y-axis. So, the equation of the hyperbola is…

Q: Find the standard equation of the sphere with the given characteristics Endpoints of a diameter: (0,…

A: Given: Endpoints of a diameter of sphere: a1, b1, c1 ≡(0, 0, 4) and a2, b2, c2 ≡(4, 6, 0)

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A: Distance between two points A(x1, y1, z1) and B(x2, y2, z2) is AB = x2-x12 + y2-y12 + z2-z12   The…