Complete the square to write the following equation as standard equation of a sphere and find center and radius of this sphere. x² + y2 + z2 – 2x + 6y + 8z +1 = 0

Q: Show that the equation represents a sphere, and find its center and radius: x? + y? + z2 – 2x – 4y +…

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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: Write the equation of the hyperbola 36x? – 25y? + 288x – 150y – 549 = 0 in standard form (x – h)?…

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

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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 equation of the ellipse consisting of points P such that P F1 + P F2 = 12, where F1 = (4,…

A: Given that PF1+PF2=12, where F1=(4,0) and F2=(-2,0)

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: Identify the surfaces of the following equations by converting them into quations in the Cartesian…

A: To identify the quadratic surface of the equation: Given: The equation of the surface is r=z2-1.…

Q: Write the equation of the hyperbola 4x2 – 25y? + 8x + 250y – 721 = 0 in standard form (x – h)? (y –…

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Q: Direction is provided for the sphere problem

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Q: Find the Center and radius of the Cirele x?+y²+4X-6y -320

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Q: complete the square to put the equation of the circle in standard form. Give the coordinates for the…

A: Given equation is x2+y2+4x−6y+12=0 First we put the equation of the circle in standard form Add both…

Q: Write the equation of a circle, in general form (x² + y² + Bx + Cy + D = 0), centered at the point…

A: The question mentions that the circle is centered at the intersection of lines, 2x+y=-10x-2y=5 Now,…

Q: name the surface represented by the equation r^2+z^2=4-2z

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Q: Find the center and the radius of the sphere. x2 +y? +z? +5x + 6z = 0

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Q: Find the center and the radius of the sphe- x2 +y? +z? + 6x – 4z = 0

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Q: Reduce the equation of the circle x +y° +&r – 9y– 6 = 0 to its standard equation.

A: Solution is written in below steps.

Q: Which of the following is a point of intersection of a circle and an ellipse with the respective…

A: Question is solved.

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: By first writing the equation in standard form, identify the traces of the surface given by the…

A: Given equation:                           x2+3y2-6y+z2+4z-3=0

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: x² + + =1 y2 9. 4

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Q: Find the perimeter of the ellipse x2/a2 +y2/b2 = 1, where a > b > 0.

A: The perimeter of Ellipse with Radii a and b is given by: In our question the radii is a and b Hence…

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

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

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Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0…

Q: Write the equation, in standard form, of the parabola containing the following points: (0, 1), (1,…

A: We will solve the following.

Q: Complete the square to find the center and radius: x^2+y^^2+8x+8y=0

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Q: find the equation of a sphere with the line segment AB as one of its diameters, where A(-3, 2, 1)…

A: We have to find the equation of a sphere with the line segment AB as one of its diameters, where…

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

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Q: x² +y? + z² + 8x – y + 5z = 2

A: solution

Q: 3) Complete the square on the circle 2.a2 + 2y? + 44.x + 28y = 52 to write it in standard form. Then…

A: Standard form of circle is given by,  (x-h)² + (y-k)² = a² , where (h, k) is the center of the…

Q: Write the equation for the above surface.

A: The surface represents the cylinder; with circle in the xz-plane. x2 + z2 = 1  (radius of the circle…

Q: Write the equation into the standard for -4.x? + y? – 16x – 2y – 19 = 0. Locate hyperbola

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Q: Find the coordinates of the points of intersection of the parabola y = x2 and y = x+3.

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Q: 1. " Identify the surfaces of the following equations by converting them into equations in the…

A: As per the company guidelines i am solving first question please resubmit the question for another…

Q: Write the equation into the standard form of the equation of the hyperbola: 2/2x? + 5V2xy + 2/2y? +…

A: As there is xy term is given so first we have to rotate the axis and eliminate that term then write…

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 point on the parabola * +y“ that is closest to the point (0, -3). =

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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: In which variable(s) should you complete the square to identify the surfacex = y2 + 2y + z2 - 4z +…

A: We have to determine which variable should we complete the square to identify the surface…

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: enter the correct answer to complete the following sentence the cirlce with the equation X2+Y2=324…

A: This is the form of a circle. Use this form to determine the center and radius of the circle.…

Q: Write the reduced hyperbole equation, given: a) The foci ( ± 5.0), and the length L=9/2 of the rope…

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Q: Write the equation of the hyperbola 9x² – 4y? – 54x + 32y – 19 = 0 in standard form (x – h)? (y –…

A: Write the equation of the hyperbola  9x2 - 4y2 -54x +32 y  -19 =0 In the standard form  (x-h)2 /a2 -…

Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: a. Consider the circle, x2 – 10x + y² – 22y + 46 = 0 i) Write the equation of the circle in standard…

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

A: Given

Q: Show that the equation represents a cirde by rewriting it in standard form, AND find the center and…

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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