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

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

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Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

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: 5. Show that the equation represents a sphere, and find its center and radius: x²+y? + z2 – 8x – 10y…

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Q: the center-radius of 9x?ー16x+9+9y?t12u=12 the equation Can be obtained by adding both sides of the…

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

A: Given: The given equation is y=2x2-5x-3 To find: we have to find the x-intercept

Q: Find the equation of the parabola with directrix x + 1 = 0, axis y = 2, and latus rectum 3. (two…

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Q: Find an equation for the indicated half of the parabola.Left half of (x + 3)2 = y + 2

A: We have the given equation of parabola   the equation is (x + 3)2 = y + 2   we have to find the…

Q: Find an equation of the sphere whose endpoints of a diameter are (-2,0, 5) and (-1,2, 3).

A: To find the length of the diameter use the distance equation Therefore, D=-2-(-1)2+0-22+5-32…

Q: Find an equation for the indicated half of the parabola.Lower half of (y + 1)2 = x + 3

A: Given equation is y+12=x+3.

Q: given the equation of parabola y^2 -8x -4y -20=0,find the length of latus rectum

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Q: 31. Find the coordinates of the focus of the parabola whose equation is x² – 18x + 24y + 273 = 0. С.…

A: Since you have asked multiple unrelated questions in a single request, we would be answering only…

Q: Find an equation for the parabola that has a horizontal axis and passes through the given…

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Q: y=2x + 8x +9 Plot five points on the parabola: the vertex, two points to the left of the vertex, and…

A: Equation of parabola in standard form is  y = ax²+bx+c

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

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

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Q: Write the equation of the hyperbola in the form -Ar (y-k)? = 1 or - a? (y-k) (x-h)² = 1. a2 2y2 - x2…

A: See in the next step

Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

A: The given data is: Suppose a golf ball is driven so that it travels a distance of 200 feet as…

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

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Q: What is the directrix of the parabola? (x – 4)? = 8 (y + 3) O x = -3 O y = -3 y = -5 x = -5

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Q: Find the center and radius of the sphere with equation (x - 6) + (y + 6) + (z + 1) = 49 Center:…

A: The given sphere equation Compare with standard equation of the sphere To find out the centre and…

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 an equation of the sphere whose endpoints of a diameter are (-2, 0, 5) and (-1, 2, 3).

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Q: Find the equation of the evolute of the parabola y? = 12x.

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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: (b) Find the evolute of the parabola y? = 4ax.

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Q: [24] Complete the square to determine the type of curve represented by the equation: 4x +9y² –16x–…

A: The given question is taken from the conic section in which we have to find out the given equation…

Q: A seagull sits atop a cliff and spies a fish under the water. To catch the fish, the seagull dives…

A: The given equation of path is y=2x2-28x+90.…

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

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Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: Find the equation of the sphere

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

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

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Q: bétween the spheres and 2- + Y 4 if the dênsity at any point is equal to the square of its distance…

A: Given: The solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4  The…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the point on the ellipse x? + 4y? + 2xy = 12 with the greatest x-coordinate. (Use decimal…

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Q: Consider the hyperbola of equation: (y – k)2 (x - h)2 1 a? 62 whose foci are (3, -1) and (3, 17),…

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Q: A parabola is modeled with the equation x2 – 6x + 4y – 19 = 0. Which is the domain and range of the…

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Q: Determine the standard equation (s) of a parabola where its vertex lies in the center of the circle…

A: Here we have to determine the standard equation of a parabola where its vertex lies in the center of…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Find the area of the largest rectangle that can be inscribed in the ellipse given by: x² + 4y? = 16

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Q: F(0,0)D:x=4  Find an equation of the parabola described.

A: Given focus=(0,0) Directrix: x=4  So the vertex is at the mid point of (0,0) and x=4 That is…

Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

A: At the points of x-intercepts, y coordinates are 0, as along x-axis y=0.

Q: d. Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (-2,…

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Q: Find the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter…

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Q: Write the equation of the parabola in the form y = a(x- h) + kor x = a(y - k) +h'

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Q: Consider the parabola given by the equation: y=x2+10x+9 Find the two values of x that correspond to…

A: Given information: The equation is y=x2+10x+9. Calculation: Find the x-intercepts of the equation…

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

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