Find the equation of the sphere passing through P(- 4, 1, 4) and Q(6, - 3, 3) with its center at the midpoint of PQ. The standard equation of the sphere is

Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Write the equation of Spheres with radius R.

A:

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

A:

Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

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: Find the equation of sphere having its centre on the line 2x - 3y = 0 = 5y + 2z and passing through…

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Q: Find the center and radius of the sphere x + y + z² +4x+6y-10z+2=0 and graph the sphere.

A: x2+y2+z2+4x+6y-10z+2=0 We need to find the center and radius of the given sphere and graph the…

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 parametric equations for the line that passes through the points P(-3,7,9) and Q(4, 1, -5).

A: The given points are P-3,7,9 and Q4,1,-5. The line containing the point x0,y0,z0 and parallel to the…

Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

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

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Q: (a) , Find an equation of the sphere that passes through the point (-3,2,-1) and centered at the…

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

A: To find the length of the diameter use the distance equation Therefore, D=-2-(-1)2+0-22+5-32…

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

A: Comparing with standard equations of sphere,

Q: Write the equation of the sphere in standard form. 9x? + 9y? + 9z2 = 36x – 12y – 24

A: The givne equation of the sphere is 9x2+9y2+9z2=36x-12y-24

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

A:

Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: . 2x2 +2y? + 2z2 = 8x- 24z +1

A:

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 that has the points (5, −2, 3) and                  (0, 4,…

A: we know that equation of sphere which has end points of diameter as x1,y1,z1 and x2,y2,z2 is given…

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

A: We have to find equation of sphere.

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: 5. Show that the equation represents a sphere, and find its center and radius:…

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Q: Find an equation of the sphere with center (1, –11, 8) and radius 10.

A: Center of sphere=1,-11,8radius of sphere , r=10Sphere has 3-dimensions ,hence equation of sphere…

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

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

A:

Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

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

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Q: Find the center and radius of the sphere with equation (x + 2)2 + (y - 3)2 + (z + 6)² = 16 Center:…

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

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Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

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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 equation of the sphere

A:

Q: Find an equation of the sphere that passes through the point (8, 1, -5) and has center (5, 6, 3).

A: The objective of the question is determine the question of sphere .

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

A:

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: Find the equation of the sphere if one of its diameters has endpoints (-3, -2, -4) and (-1, 2, 2)…

A: Given: The endpoints of one of its diameter are -3,-2,-4 and -1,2,2. The coefficients of x2 is 1.

Q: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

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

A:

Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 3, – 2). O…

A: We know that,  General equation of sphere is given by, (x-a)²+(y-b)²+(z-c)²= R² where, R is the…

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

A: