Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of two sheets. O A hyperboloid of one sheet. O A hyperbolic paraboloid. O An ellipsoid. O An elliptic cone. O An elliptic 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: . Use the method of completing the square to write the following equation in standard form and…

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Q: 5. Calculate the area of a regular hexagon inscribed in a circle of radius 1 unit. a. 1.316 units b.…

A: Area of equilateral triangle = 34 a2 ; where , 'a' is the sides . Note : As per our Guidelines , we…

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: Identify the quadric surface each of the following equations represent and sketch its graph. O 92" +…

A: 9 x2 + 4y2 + 36 z2 = 369 x236+4 y236+36 z236=1x24+y29+z21=1x222+y232+z212=1

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: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

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: The plane 9x + 12y + 40z = 275 intersects the cone z? = x² + y? in an ellipse. The sum of the…

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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: Reduce the equation to one of the standard forms, classsify the surface,and sketch it. x2 - y2 - 4x…

A: Given : equation x2-y2-4x-2z+3=0To find : reduce the equation in standard form, classify the surface…

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

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Q: Which quadric surface is this? *- ² + = 1 | Hyperboloid of One Sheet Hvnorholeid of Two Shoots

A: We are asked to identify the quadratic surface,

Q: 3. Find the center and radius of the sphere having the equation: x²-4x+y² +8y+z² – 2z=4

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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: Find the center and radius of the sphere (3x^2)+(3y^2)+(3z^2)-(6y)-(12z)-10=0

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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: For the quadric surface, - + z = = 1, setting the value of z = 1will give you which conic section? 4…

A: The given quadric surface is x24-y29+z=1  To find when z=1which conic section represents the…

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: II. Solve the following. Slems. 1. 2. Name and sketch the graph of the surface with equation +z2 –÷=…

A: Given

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

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Q: What is the second coordinate of the center of the sphere of the equation below?…

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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: 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: 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: 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: 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: 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: 32. Which of the following is the trace of the surface in the plane y=3? Hyperbola Ellipse Parabola

A: Consider the given surface as 9x2+z2-3y=0

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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