Find the equation of the sphere passing through P(-8, 5, 8) and Q(6, -7, 7) with its center at the midpoint of PQ. The standard equation of the sphere is . (Simplify your answer.)

Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: The general equation of the sphere is given as x-x02+y-y02+z-z02=r2. Here, the center of the sphere…

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

A: On simplification, we get

Q: The general formm of an equation is r+y-+3y+1%3D0. What is the equation of the circle in standard…

A: Using general & standard form of circle

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

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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 the parametric form of (i) the circle x?+y? =p²

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

A: Equation of sphere with Centre (a,b,c) and Radius 'r' can be written as: x-a2+(y-b)2+(z-c)2=r2 Using…

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

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Q: Which point or points on the ellipse x? +4y? = 4 are furthest away from the point (0, 1)?

A: The Equation of the given ellipse is, x2+4y2=4 Let the furthest away point on the ellipse, from the…

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

A:

Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

A:

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

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

A:

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2…

A: Given: x2 + (y - 2)2 + (z - 2)2 = 4

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

A: The given equation of sphere is: x2+y2+z2+9x-2y+10z+23=0

Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

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Q: 3x2 − 6x − 4y + 8 = 0 identify the standard form, vertex, focus, ends of latus rectum, directrix;

A: the solution is following.

Q: Write the equation for a sphere centered at the point (7, – 1, – 5) and has the point (6, – 8, – 9).

A: *** This is the problem related to Analytical geometry 3D and we are advanced math expert and have…

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

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Q: Show that the equation represents a sphere, and find its center and radius: x²+y² + z² – 8x + 6y +…

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Q: What is the directrix of the parabola? (z+3) =8 (y-1) O y= 3 O y=2 O y= 1 o y=-1

A: If General equation of parabola :  y = a ( x - h ) 2 + k  Then directrix y = k - ( 1/4a )

Q: Write the equation for a sphere centered at the point (6, 1, - 3) and has the point (10, - 2, -8).

A:

Q: Find the standard equation of the sphere that has the point (-3, - 6, 0) and (3, 4, 5) as endpoints…

A: Given : The point (-3, -6, 0) and (3, 4, 5) as endpoints of a diameter of sphere.

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 5x - 2y +…

A:

Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A: Given: Corners of the reference rectangle: (8, 7), (−6, 7), (8, −3), (−6, −3); Horizontal transverse…

Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

A:

Q: ^2+84x-24y

A: Given Ellipse: 21x2-4y2+84x-24y=36This equation can be re-written as-21(x2+4x)-4(y2+6y)=36 To find…

Q: Find the equation of the sphere

A:

Q: Express the general form to its standard form and locate the center, vertices, covertices and foci…

A: equation 4x2 - y2 - 32x - 4y + 24 = 0

Q: Write the equation of the sphere if (3, 4, 7) and ( - 5, 6, – 3) are the end points of a diamter of…

A: (3,4,7) and (-5,6,-3) are the end points of the diameter of a sphere.

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

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Q: Determine whether the following equation represents a sphere.

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Q: Find the radius and centre of the sphere x + y + – 4x + 2y-6z-11=0.

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

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Q: form- State the coording center of the circle and x²-2x+y²-4y-12=0

A: Given  Equation of the circle x2-2x+y2-4y-12=0

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: c) Find the center and radius of the sphere whose equation is x2 + y? + z? + 10x + 4y + 2z – 19 = 0

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Q: Find the centre and radius of the sphere determined by the equation x' +y° +(z - 2) = 16 %3D

A:

Q: Find the centre and radius of the sphere determined by the equation x'+y* +(:-2)° =: 25

A: Given that sphere equation is - X2 + Y2 + (Z - 2)2 = 25 And we find radius and centre of the sphere.…

Q: For the three points ( 1,5), (2,9) and (-1, 7), find a quadratic model y = ax + bx + c through the…

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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 a or k so that the points (-5,-8) and (1,-25) lie on the parabola y=a(x+3)²+k

A:

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 5x - 2y +…

A: Given

Q: Given 4x2 + 9z2 = 9,2 (a) Write the equation above in standard form. (b) Identify the surface. (c)…

A: We have to  write the equation in standard form, name the surface, find its axis, sketch the…

Q: c) Find the center and radius of the sphere whose equation is x² + y? + z? + 10x + 4y + 2z - 19 = 0

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Q: Given the equation of all points equidistant from a center, what is the center point? (x – 3)² + (y…

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Q: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A: From the given statement, the corners of the reference rectangle are  (7,6), (-1,6), (7,0), (-1,0)…