1. Complete the square to transform the general form equation below to standard form in order to determine the center and radius. 4x2 + 4y2 – 16x – 24y + 51 = 0

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

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Q: 14. Which equation represents the given parabola? O y = -4(x – 4)² + 5 O y = }(x – 4)² + 5 O y =…

A: First option is correct.

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

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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: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

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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: 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: nd an equation of a sphere if one of its diameters has endpoints (54.

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Q: Q.1/ a- Find the radius and center of the equation 9x2 + 9y² - 6x - 107 = 36y %3D

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

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Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Write the equation of the sphere in standard form. 9x? + 9y? + 9z2 = 36x – 12y – 24

A: The givne equation of the sphere is 9x2+9y2+9z2=36x-12y-24

Q: be the equation 12x2 + 12x y + 7y2 − 4x + 6y − 1 = 0. a)  Determine the nature of the conic. b) Find…

A: The solution are next step

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: Given the equation x² + y² – 8x + 4y + 11, = 0 find the standard form equation in the form (x – h)²…

A: The solution is given below.

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

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Q: Convert the following equation for a hyperbola into standard form. 64x2 – 128x – 16y? – 64y – 1024 =…

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

A: The given equation of sphere is: x2+y2+z2+9x-2y+10z+23=0

Q: 29. What is the center of the circle in the standard form (x- 6)² + (y-1)2 = 81? а. (6,1) %3D b.…

A: We need to find the radius and center of given equation of circles

Q: 5. Show that the equation represents a sphere, and find its center and radius:…

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Q: Verify that the circles x² +y? – 4x – 7y +6 = 0 x² +y? + 3x – 14y – 1 = 0 and, 3(x2 + y?) + 2x – 35y…

A: Given:   Let S1=x2+y2-4x-7y+6=0         S2=x2+y2+3x-14y-1=0         S3=3x2+y2+2x-35y+4=0    Now,the…

Q: 8: Which one of the following conics is a parabola? 22 + y + 5 = 4æ B 222 + y? = 4x +4 4r – 9y? +…

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

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Q: a) [ Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: The three-dimensional quadric figure below is described by: x² + 2y? + 2z – 5 = 0

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

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Q: 20 (0, 3) %23 -4-2 2468 4 to (3,-6) Write the standard form of the equation of the parabola shown at…

A: From given vertex write the standard form of equation of parabola and than satisfy the given point…

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

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Q: III. Transform the equation of the parabola to the standard vertex for: completing the square. 16.…

A: Since we are given with multiple number of question and our guideline is solve first question only…

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

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Q: 1. Convert this equation into ce form State the coordinates center of the circle and its r…

A: Answer

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

A:

Q: Draw the hyperbola with the equation: 3x? – 2y² + 6x – 8y = 6. %3D

A: Given: 3x2−2y2+6x−8y=6

Q: What is the equation of the given parabola? y 4 -5-4-3-2 1 2 3 4 5 A y= 3x² 6x +3 I23 45

A: Here zeros form equation y=a(x-p)(x-q) p,q are zeros of equation

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

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Q: 2. Which of the equations below also represents the parabola y=-3x² 18x + 16? Oy=3(x+3)² +65…

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Q: A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is…

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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: Which one of the following conics is a parabola? A 2 +y+5 = 4x B 22 + 3 = 4x +4 C 47 – 9y? + 32x –…

A: Any equation of the form Ax2+Bxy+Cy2+Dx+Ey+F = 0 , then it forms a parabola if and only if A = 0 or…

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

A:

Q: Identify the quadric with the given equation and give its equation in standard form. x2 + y2 + z2 -…

A: x2+y2+z2-4yz=1

Q: be the equation 12x2 + 12x y + 7y2 − 4x + 6y − 1 = 0. a)  Determine the nature of the conic. b) Find…

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: 1. Find the distance between the points A(1,2) and B(3,4) in simplest radical form.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 5. Write the following equations in standard form and identify the corresponding conics a) x² – 4x +…

A: The given equations can be converted into standard forms by the method of completing square of x and…

Q: 3. Write the equation into the standard form of the equation of the hyperbola: x² – 4xy + y² + 8x +…

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