Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y + 5z - 6 = 0, x + 2y – 7z = 0 lie on the same sphere and find its equation.

Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

Q: By completing the square, put the equation 2 – 64y tử + 42 – 16z = –68 Into the standard form…

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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: What is the center of the sphere given by the equation x² − 6x + y² – 2y + z² + 8z + 17 = 0? -…

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Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

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

A: We have to find

Q: 1. Find the equation (formula) of a sphere with radius r and center C(h, k, 1) and show that x² + y²…

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Q: Find the equation of a circle in standard form whose center is at (-4,3) and radius v5 * O…

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Q: (x+5)^2 + (y+12)^2 = 49 The given equation represents a circle in the xy-plane. If the circle is…

A: We have to translated up by 2 units

Q: The equation x² + 14x + y² – 8y +z2 +10z = – 65 represents a sphere whose center is (-7,4, – 5) |

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Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

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: The equation of the sphere with Center (4,-1,3) and radius √5 is

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Q: Find the center and radius of the sphere: 3x² + 3y² + 3z² -6x - 12y + 18z + 150 O Center (1, 2, -3);…

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