The surface of equation + 1 is: 16 A circular cylinder An ellipsoid

Q: 4. The upper half of the ellipse centered at the origin with axes of length 2a and 2b is described…

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Q: Find the equation in rectangular coordinates of the quadric surfaceconsisting of the two cones φ =…

A: The relation between spherical and rectangular coordinates in polar form is given by the following…

Q: The surface of equation= ++ = 1 is: - 4 16 An ellipsoid A circular cylinder A cone A sphere

A: Equation of ellipsoid

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 9) Radius:…

A: Given:Center : (-1,-2,9)Radius: 7We will find the equation of the sphere

Q: Find the standard equation of the sphere with the given characteristics. ...... Center: (-1, -3, 7)…

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Q: 7. The parametric equation of an ellipse is given by x = a cost, y=bsint; 0<t<2n. Determine the area…

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Q: The plane x+ y+2z =2 intersects the paraboloid z = x2+y² in an ellipse. Find the points on this…

A: Given a plane x+y+2z=2 intersects the paraboloid z=x2+y2 in an ellipse We need to find the points on…

Q: 2. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? Oy = 4(a- 1)2 + 3…

A: Here, the parabola is of the form (x-h)2=4a(y-k) Whose focus is given by (h,k+a)=(1,4) given…

Q: Identify the type of surface represented by the equation z2 x2 %3D 10 10 6. Parabolic cylinder…

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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…

A: The given equation is z22-x28=y2. As we know that the general equation of the parabolic cylinder is…

Q: A hyperboloid of two sheets Graph the surface defined by the equation - 16x? – 4y? + z? + 64x – 80 =…

A: Given: A hyperboloid of two sheets:  – 16 x 2 – 4 y  2 + z 2 + 64 x – 80 = 0.   To sketch: The graph…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 7) Radius:…

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Q: Find an equation for the surface obtained by rotating the parabola y=2 about the y-axis.

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Q: 57. Use a change of variables to prove that the area of the ellipse with equation (-) + ) : -1 is…

A: Explanation: Given that, the standard equation of the ellipse is: x2a2+y2b2=1 Solve for…

Q: The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on…

A: Given the plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. We need to…

Q: Find the center and foci of the ellipse. (x+5) (y+9)² = 1 %3D

A: The given ellipse equation,(x+5)25+(y+9)29=1

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -3, 5) Radius:…

A: We are given: Centre: (-1, -3, 5)Radius: 7 We need to find the standard equation for the sphere with…

Q: The surface of equation + = 1 is: A cone O An ellipsoid O A sphere O A circular cylinder

A: The given equation is, x24+y29+z216=1

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 8) Radius:…

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Q: What is the highest point on the ellipse that is the intersection of the plane x + y + 2z = 2 and…

A: Given  the intersection of the plane x+y+2z=2 and the paraboloid z=x2+y2

Q: Determine the equation of ellipse in standard form with center (2,3), semi-major axis is 5, vertical…

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Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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Q: 2. Which conic section is represented by the équation 2x2 + 4x- y +9 = 0? O Hyperbola Ellipse O…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, =7,2) Radius:…

A: Explanation of the answer is as follows

Q: Find the center, vertices, foci, and eccentricity of the ellipse. x2 y? 169 144 center (х, у) -…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 9) Radius:…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: Find the equation of the surface of revolution that is generated by rotating the parabola y = x^2…

A: Equation of surface of revolution of a curve about y-axis is given by x2+z2=r2 where r is the radius…

Q: Find the center, vertices, roci, and eccentricity of the ellipse. x2 y² = 1 121 49 center (х, у) %-…

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Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: Sketch the graph of the equation in xyz coordinate system and identify the surface 8x? + 4y? – z2 =…

A: Sketch the graph for the given surface.

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -9, 3) Radius:…

A: To find the standard equation of sphereCenter: -1, -9, 3Radius: 4

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –3, 5) Radius:…

A: Given that: Centre of the sphere, (h,k,g)= (-1, -3, 5) and radius, R=6

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 4) Radius:…

A: Equation of sphere

Q: The equation of a surface is shown below. Which among the choices best describes the surface…

A: For the given statement

Q: The parabola has focus (0,-2) and directrix y=2.

A: equation of parabola with focus ( a , b ) and y = c  is given as below : here a = 0 b = -2  c = 2

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: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

Q: A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and…

A: It is given that, A mirror for a reflecting telescope has the shape of a (finite) paraboloid of…

Q: find the standard equation of the sphere with center (4,3,3) and radius 7

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Q: Identify the surface generated by the equation 9y^2 + 4x^2 - z^2 = 36 hyperboloid of 1 sheet,…

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Q: The surface of equation + + = = 1 is: 16 A cone An ellipsoid A circular cylinder OA sphere

A: The explanation of the solution as follows:

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed in the ellipse x2/a2…

A: Let 2x,2y be the length and width of the ellipse that is inscribed in ellipse  Then , perimeter of…

Q: Find the envelope of the family of ellipses x2/a2+y2/b2=1 having the same area.

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -2, 7) Radius:…

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Q: The surface of equation – +- 1 is: 16 A sphere O A cone O An ellipsoid || + 이닙

A: We can explain it as below using the concept of three dimensional geometry.