If a bug walks on the sphere 2 +y+ z² + 2.x- 16y-2z- 103 = 0 how close and how far can it get from the origin? NOTE: Enter the exact answers. Largest distance3D Smallest distance3D

Q: The following hyperbolas are confocal: x2/4 –y2/8 =1 and x2/6 –y2/k =1. What is the value of k

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Given sphere A₂: x² + y² + z² - 16x + 6y - 4z + 76 = 0 1. Solve for the center and radius of sphere…

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Q: find the center and radius of the sphere x^2+y^2+z^2+8x-8y+6z=-16

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Q: Choose the equation that represents the graph of the quadric surface below 3. 21 O z = 4 - 5y2-92 O=…

A: From graph we see that the quadric surface represents a paraboloid whose axis is y-axis Here 1st…

Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

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 radius of the sphere. x2 +y2+z2 - 16x - 12y + 6z = -45

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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: C) lie in the parabola 16y = 160 – x². Find the maximum area of the triangle if side rtices B and C…

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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: Find the point on the sphere x2+y2+z2=1089 that is farthest from the point (-22,-17,-21).

A: Let, (x,y,z) be the point on the sphere g(x,y,z)=x2+y2+z2-1089=0...(1) which the maximum distance…

Q: Write the sphere in standard form. 4x2 + 4y2 + 4z2 − 32x + 16y = 1

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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,

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Q: 18. Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. show solution

A: It represents hyperboloid.

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

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Q: The equation of the sphere with center (2,-3, 10) that touches that y-axis is OA (x- 2)° + (y +3)* +…

A: Solution is given below:

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y = 7…

A: here the width of the rectangle is  w=2x and the right is l=7-x2

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: The equation of the sphere with center (4,-2, 9) that touches that -axis is OA. (x – 4)* + (y + 2)*…

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Q: Find the center and the radius of the sphere. x2+y2+z2-3x-6z=0

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Q: Find the point on the sphere x2+y2+z²=529 that is farthest from the point (-7,-11,-29).

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Q: c) Find the center and radius of the sphere whose equation is x² + y² + z² + 10x + 4y + 2z – 19 = 0

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Q: Find the radius and center of the sphere described by 3x2 + 3y2 + 3z2 + 6x – 6y = 3.

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

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Q: Show that the equation represents a sphere, and find its center and radius: x^2+y^2+ z^2-8x + 6y +…

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

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Q: 3. Find the center and radius of the sphere having the equation: x²-4x+y² +8y+z² – 2z=4

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Q: 2. Does the equation x² + y² + z²-3x - y + 3z = 0 represent a sphere? If so, find the center and the…

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Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 4, 12). OA.…

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Q: 2. Find the center and radius of the sphere *+y ++4x-2y+8-4 0

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Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: Find the radius and center of the sphere. x2 + y² +z² - 6x + 8y – 4z = - 13 r=

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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: The equation of the sphere with center (3,-10, 9) that touches that y-axis is OA. (r-3)2+ (y 10)+…

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

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Q: Find the center and radius of the sphere x2 + 18x + y? + 4y + z2 + 10z = –74 Center: ( || ) Radius:

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Q: Which of the following represents the radius of the sphere whose equation is x² + 8x +y2 – 16y +z² –…

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Q: 9. Find the center and radius of the sphere given by 3x + 3y? + 3z2 = 10 + 6y + 12z.

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

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Q: find the ends of the latus rectum, axis of symmetry of x2+20y=0

A: Given  x2+20y=0 Find the ends of lactus rectum and axis of symmetry.

Q: How to find the maximum and minimum points on the sphere?

A: Maximum and Minimum points will occur where derivative will be zero for teh function. In case of…

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

A: We will find the equation of sphere as following.

Q: Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point…

A: Given sphere, x2+y2+z2=1 Consider gx,y,z=x2+y2+z2-1=0 The square of the distance between the points…

Q: find the equation of a sphere. x^2 +y^2 + z^2 +2x - 2z -2 = 0

A: see the details solution in below

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

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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…

Q: - The equation of the sphere centered at C(h, k, l) and radius r is given by (x − h)² + (y − k)² +…

A: The given sphere equation x2+y2+z2-4x+2y+6z-11=0