Complete the square to write the following equation in the standard form for a sphere. x²+y² +z²-2x-8y+4z+20=0 a. (x+1)²+(y-4)² +(z+2)? = 20 b. (x-1)²+(y+4)²+(z+2)² = 1 e. (x-1)²+(y-4)² +(z+2)? = 1 d. (x–1)? + (y-4)² +(z+2)? = 1

Q: Write the equation of the hyperbola 25x? – 9y? + 100x + 72y – 269 = 0 in standard form (z – h)? (y –…

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Q: Nhat is the equation of the parabola containing the points (2, 2), (4,-8), and (-2, –14)? O y = - 4x…

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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: Find the center, vertices, foci, and sketch from x -4y2 +6x +16y -11 = 0.

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Q: Identify the surface with equation 9x2 – 4y?+ 16z2 – 144 = 0.

A: Given: The equation 9x2-4y2+16z2-144=0 To find: The name of type of surface with the given equation.

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 parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

Q: 7. x2 +y? +14x- 12y + 4 0 %3D Center : (_and radius:

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the focus of the parabola (y + 2)2 = -16(x 3). O(7.2) O(6.3) O (3,-2) O (1-2)

A: We have to find the focus of the given parabola. The solution is following.

Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: vertex of parabola : (-2,1)= (h,k) x=a(y-k)²+h ✓ (-1.5, -2.3) (j,4.2)

A: Given Vertex of parabola h, k=-2, 1 Equation of parabola x=ay-k2+h Points of intersection of line…

Q: Write the equation of the hyperbola 9x² - 36y2 - 18x144y - 459 = 0 in standard form (x - h)² (y -…

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Q: 3. Select the parabola that matches the quadratic relation y = x + 3x + 2. a. C. b. d.

A: We have to find

Q: Find the focus of the parabola y2 - 8x + 4y + 28 = 0. Select one: O a. (5, - 2) O b. (3, - 2) O c.…

A: We have to find the focus of the parabola

Q: x2 + (y − 4)2 = 1   Write the equation of the circle in standard form, (x − h)2 + (y − k)2 = r2.

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Q: In which direction does the parabola x = -y 2 + 3 open?

A: x=-y2+3 There are two patterns for a parabola, as it can be either vertical (opens up or down) or…

Q: Find the equation of parabola given these three points using quadratic formula. (1,27) (18,45)…

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Q: Complete the square to write the following equation as standard equation of a sphere and find center…

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Q: Determine the focus of the parabola (x - 2)² = 4(y - 3). %3D O (-1,-3) O (2,4) O (-2,-2) O (2,3)

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Q: Rewrite the given equation of a quadratic surface and identify the graph. 9y2 + z2 = 4x² – 36

A: We want to identify the given equation.

Q: Convert the following equation into vertex form by completing the square. x2 - 18x +21 O (z- 8) + 21…

A: The explanation of answer as follows

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: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

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: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

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

A: We will solve the following.

Q: Show, by completing the square, that the parabolay = ax2 + bx +c can be obtained from y = ax 2 by a…

A: The given equation of parabola is y=ax2+bx+c. Rewrite the above equation as follows.…

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

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Q: Complete the square to find the vertex of this parabola. x² – 12y – 6x + 5 = 0 3,-

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Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

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Q: Convert the equation to the standard form for a hyperbola by completing the square on x and y. a2 -…

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Q: Complete the square to find the center and radius: x^2+y^2+2x+4y-1=0

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Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x -

A: Rewrite the equation as z2 in terms of x and y.

Q: 6) Use the process of completing the square to transform the General Form equation below into…

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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: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

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Q: Complete the square to write the equation of the sphere in standard form. Find the center and…

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Q: 6) Use the process of completing the square to transform the General Form equation below into…

A: Given,  x2+y2−10x−16y+53=0Concept used:x2−2ax+a2=x−a2

Q: Use the method of completing the square to change General form to vertex form В. y = x + 8x + 3

A: “Since you have posted a question with multiple subparts, we will solve the first three sub-parts…

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: For the three points ( 1,5), (2,9) and (-1, 7), find a quadratic model y = ax + bx + c through the…

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Q: Write the following equations of parabola in the standard form. a. y = -4(x + 2)² – 3 b. Зу — 9х +…

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Q: Complete the square to determine whether the graph of the equation is a parabola, hyperbola, circle,…

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Q: Write the equation of the hyperbola 9a- 16y² – 18x + 160y – 535 = 0 in standard form (x – h) (y– k)°…

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Q: What is the distance between the vertices of the ellipse: 64x^2 + 25y^2 _ 16x - 16y-648= = 0? C.…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.