Question 2 Given the equation −4x² + 8x − 4y² − 56y − 4z² + 32z = -312 a) Show that the given equation represents a sphere, and find its center and radius. b) Determine whether the point (5, -8,4) lies inside/ outside / or on / the sphere.

Q: Consider the following equation of a circle written in expanded form. x² + y² + 4x+10y = - 4 Whic…

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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: Identify the surface with equation 9r? - 4y? + 16z? - 144 = 0. %3D

A: Given the equation : 9x2-4y2+16z2-144=0 We know Equation of hyperboloid of one sheet:…

Q: Find the center and the radius of the circle with the equation x2 + 10 x + y² + 8 y – 128 = 0 Enter…

A: Given : x2+10x+y2+8y-128 = 0

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

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: How do you write an equation of a sphere with a given center and radius?

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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 center and radius for the equation (x - 4)² + (y + 6)² = 81 ?

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Q: Determine whether the graph of the given equation is symmetric with respect to the x-axis, the…

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Q: Completing the square is needed to rewrite the general equation of the circle into the standard form…

A: The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is…

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: Given the equation (z+2) + (y- 15) - 144, identify the center and radius. Do not enter any spaces…

A: Given circle equation is (x+2)2+(y-15)2=144  We know the standard form of circle equation is…

Q: cirrF Find the equation to the sphere through the circle x + z? = 1, x + 2y + 3z = 4 and the origin.…

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Q: What are the center and radius of the circle described by the equation x2 + y2 + 6x + 10y + 18 = 0?…

A: Find your answer below

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

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Q: A circle has a circumference of 10n inches and a center of (9, 2). What is the standard form…

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