a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its center and the radius.

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: . Use the method of completing the square to write the following equation in standard form and…

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Q: Find the equation of a sphere if one of its diameters has endpoints: (-10, -12, -13) and (4, 2, 1).…

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

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Q: Given the equation (z - 13)+y? = 64, identify the center and radius. Do not enter any spaces when…

A: In this we have to tell the center and radius of circle.

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: Recall that an equation of a circle can be written in standard form (x-h)² + (y-k)² = r, where (h,…

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Q: Complete the square to write the following equation in the standard form for a sphere. x²+y²…

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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: Complete the square method: Show all your work! Put x² + y² 10x + 6y 15 = 0 in center radius form.…

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Q: What is the equation for a sphere centered at the point (4,-3,-7) with a radius of 5.

A: The general equation for a sphere in three dimensions is given by (x - h)^2 + (y - k)^2 + (z - l)^2…

Q: Write the equation 4x² - 25y²-2² - 100 = 0 in standard form. Draw a sketch of its graph and name the…

A: Please see the below pictures for detailed solution.

Q: What is the Discriminant of the equation x- 3x + 2-0? and what does it represent?

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Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

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

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Q: Prove that a·a= = |a|2, where a is a vector with n components

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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 equation x² + y² + 2² − 8x + 4y + 2z -4 = 0 is a sphere, a point, or a null…

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