Identify the surface by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic paraboloid. O A hyperboloid of two sheets. O An elliptic cone. O An ellipsoid. O A hyperbolic paraboloid.

Q: Find the center and radius of the sphere x? + y? + z? - 6y + 8z = 0 Find an equation of the sphere…

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

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

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Q: Let a > 0 and b > 0. Show that the area of the ellipse x2/ a2 + y2/ b2 = 1 is ab

A: Given that, The equation of the ellipse  x2/ a2 + y2/ b2 = 1 , where a > 0 and b > 0. Solve…

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: An insect is tracing an elliptical boundary of a hot plate. The ellipse equation is given by+ = 1.…

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Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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Q: State the type of the quadratic surface: ()' - (5)' + (¿)° = 1 2 1. Ellipsoid 2. Hyperboloid of one…

A: Here we need to find the type of quadratic surface and it's trace obtained by the plane z=1

Q: Identify the quadric surface and sketch the graph. z = x2 + 4y2

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Q: 1. Find the center and radius of the given equation of the sphere. x + y +z´ - 4x+ 6z+12=0

A: Given: The equation of sphere is x2+y2+z2-4x+6z+12=0.

Q: What is the directrix of the parabola? (x + 3)² = 8 (y – 1) y = 3 O y = 2 O y = 1 O y = -1

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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: State the type of the quadratic surface: (중)"- (1)" + (주)'=1 1. Ellipsoid 2. Hyperboloid of one…

A: NOTE: Refresh your page if you can't see any equations. . here two of the variables have positive…

Q: The plane 6x + 8y+ 60z = 700 intersects the cone z? = r? + y? in an ellipse. The sum of the…

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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: Find the vertex, force, and directrix of the parabola x^2=7y

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Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: y? = t2 – 2t and x = t + 2 is I. Ellipse II. Circle III. Parabola IV. Hyperbola

A: topic - conics

Q: What is the center of the hyperbola? (y+3)? 9. (x-2)2 =D1 2 Enter your answer by filling in the…

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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 the radius of the sphere. x2+y2+z2-3x-6z=0

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Q: find the perimeter of the ellipse x2/a2 + y2/b2 = 1.

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: Given a cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of…

Q: c) Find the center and radius of the sphere whose equation is x² + y² + z² + 10x + 4y + 2z – 19 = 0

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Q: 4 SKetch the parabola and label the foces , ventees and dineder 2. 4 -6y -2utl=0

A: To find- Vertex, focus and directrix of a given parabola.

Q: Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(r, y, z) = x²i +y²j+ z²k.

A: The vector field is Fx, y, z=x2i+y2j+z2k. The curve C is x+32+5y-22=16. Obtain the parametric…

Q: What is the directrix of the parabola? (z+3) =8 (y-1) O y= 3 O y=2 O y= 1 o y=-1

A: If General equation of parabola :  y = a ( x - h ) 2 + k  Then directrix y = k - ( 1/4a )

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

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Q: Find the coordinates of the four points at which the hyperboloid of one sheet given by x2 y? + 16 z?…

A: This question is related to 3D coordinate geometry, We will solve it using given information.

Q: Which of the following quadric surfaces most resembles a football or rugby ball? Select one: O a.…

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: Find the directrix for the parabola. y = 20 (x+ 2)² - 3 1- x= -1 O y = -1 O y = -8 y 3= O x = -8

A: We will find out the required equation of directrix.

Q: 2. Find the center and radius of the sphere *+y ++4x-2y+8-4 0

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Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: A landscape architect is designing an elliptical pool that will fit in the center of a 20-by-30-…

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Q: Find the area of the ellipse given by x2/64+y2/ 4=1. Area =

A: Solution: The objective is to find the area of the ellipse given by x264+y24=1

Q: Find the radius and centre of the sphere x + y + – 4x + 2y-6z-11=0.

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Q: Identify and sketch the surface -25x^2 +4y^2-100z^2=100.

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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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: A surface in space is defined by the equation x2 – y? + z2 + 5 = 0. Which one of these is true? The…

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Q: (a) Find and identify the traces of the quadratic surface x2 +y2 -z2 =1 and explain why the graph…

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Q: Consider the ellipse given by the intersection of the plane x+y+7z=3 with the paraboloid x^2+y^2=2z.…

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Q: What is the length of the minor axis of the ellipse: 5(x+2)2+(y-0.1)2=125? a. 8 units b. 12 units…

A: Given the length of the minor axis of the ellipse 5(x+2)2+(y-0.1)2=125. Let us convert the equation…

Q: 5. What is the general form of an ellipse with foci at (0, +2), and vertices at (0, ±4)? 2x + 4y = 0…

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

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

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Q: Describe the 3-space graph of the equation z? = y? + x². O A. a circle having radius z in the…

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Q: Find the vertices and foci of the ellipse. x2 + 3y2 + 2x – 6y + 1 = 0 vertices (x, y) = (smaller…

A: Standard form of ellipse x-h2a2+y-k2b2=1 Foci = h±c,k, where c=a2-b2 Vertices = h±a,k