State whether the equation () + ()ʻ + 4z² : = 1 defines a paraboloid (elliptic) an ellipsoid a hyperboloid of one sheet a paraboloid (hyperbolic) a hyperboloid of two sheets an elliptic cone Describe the trace obtained by intersecting with the plane x = a hyperbola an ellipse O a parabola

Q: State whether the equation 2 = (;)° – ()' lefines (enter number of statemer .A hyperbolic paraboloid…

A: The given equation is z2=x32-y52

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Q: A hyperbola centered at the origin of the xy-plane has vertices (0, +3) and eccentricity 2. F ind…

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Q: (a) Find and identify the traces of the quadric surface  x2 + y2 − z2 = 81  given the plane. x = k…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: Eliminate the parameter and obtain the standard form of the rectangular equation. Ellipse: x = h + a…

A: We find cos theta and sin theta from the given equations. Then put them in the Pythagorean identity…

Q: 7) Determine the shape of the I point parabola with focus F(2,5/2) and directrix line y=7/2. *

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Q: The reflector of a searchlightis in the shape of a paraboloid of revolution. Its diameter is 32…

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Q: Identify the quadric surface as an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets,…

A: We need to find values of a,b,c.

Q: Give ONE example of a plane P that is parallel to one of the coordinate planes (the ry-, xz- or…

A: The given equation of the Hyperboloid can be modified as shown below: x28-y24-z23=1    ⇒…

Q: Solve for the standard equation of the given charactensti complete solution hen graph and label all…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 0 1) Find an equation of the trace of S on…

A: let S be the surface with equation 4y2+4z2-x2-16=0

Q: (e) 25z = x² + 25y²; %3D a = i ,b = i ,C = (f) z? – x² – y² = 1; h = >

A: Topic:- 3D-Geometry e) Elliptic paraboloid f) Hyperboloid of two sheets

Q: The are of the parabola y=x² from (1, 1) to (2, 4) is rotated about the y-axis. Find the area of the…

A: Let's find area of the resulting surface.

Q: 5. Find equations for all the planes that intersect the y-axis at y = 1 and the z-axis at z = 2, and…

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Q: center, horizontally, is the car when it is at an altituue Ul 23 IL! 2. A truck has to pass under an…

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Q: Determine the center-radius form of the equation of a sphere which circumscribes two externally…

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Q: Find the area of the resulting surface if an arc of a parabola y=x2 from (1,1) to (2,4) is rotated…

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Q: A semielliptical arch over a tunnel for a one-way road through a mountain has a major axis of 50…

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Q: 17. Find an equation in standard form for the circle centered at (7,–2) with radius 8. A. (x – 7)² +…

A: I have appended the formula used in the solution part.

Q: hyperbolic paraboloid by matching the equation with one of the forms given in Table 11.7.1. State…

A: As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: Module 9: Conic Scctions 4. What are the center and radius of the circle given by x2 + y - 16x + 8y…

A: Find the radiuss and centre of the circle by comparing with the standard form of the circle

Q: The paraboloid z= 6-x-x2 -2y2 intersects the plane x=1 in a parabola,Find parametric equations for…

A: The paraboloid z=6-x-x2-2y2 intersects the plane x=1 and we get the parabola z=4-2y2 in the plane…

Q: 5. Find an equation of the sphere with center (4, −8, 4) and radius 5. Use an equation to describe…

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Q: State whether the equation 3x? – 3y² – 5z² = 1 defines | an elliptic cone. an elliptic paraboloid.…

A: As per our guideline i am supposed to answer only one question from these two images which contain…

Q: 3) Find the family of curve that intersects the family of hyperbolas y = 2r+b at an angle arctan(1)…

A: Given the equation of family of hyperbolas is y2=2x2+b

Q: Identify the type of quadric surface defined by the equation +z= 1, 36 and find all x-, y-, and…

A: Given surface is  y24-x236+z=1                    (i) which is a parabola So, the Quadric surface…

Q: a) x² x² + y² - 2² +22=1 ɔ) x² − y² + 2y + z² = 2 =) x² 4x − y² — z² = −3 d) x² - 4x − y² — z² = −4…

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Q: 4. (a) Find the tangent line to the limaconr = 2 + 4cos0 at pole. Also find the points on the…

A: 4(a)

Q: 4. State a parametric representation of the hyperbola whose equation is given that will satisfy the…

A: Equation of hyperbola = x29 - y24 =1

Q: A bridge is built in the shape of a parabolic arch. The bridge has a span of s = 180 feet and a…

A: Given Shape of the bridge is parabolic. Span of the bridge=180 feet Maximum height=25 feet

Q: give the eccentricities and the vertices or foci ofhyperbolas centered at the origin of the…

A: The standard form of equation of hyperbola centered at the origin, is given by  x2a2-y2b2=1 ( When…

Q: 5. Complete the following table. Length of Length of transverse conjugate axis Equations of the…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Consider the equation below. 2y2 + z2 - x - 8y – 4z + 12 = 0 (a) Reduce the equation to one of the…

A: Consider the equation…

Q: A surface in space is defined by the equation 2 + z? = 4. Which one of these is true? The surface is…

A: The given equations is x2+z2=4

Q: O An ellipse in the plane x axis, minor axis of length 14 parallel to the y-axis. = 1, center at (1,…

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Q: 1. Let A be the sphere having diameter with endpoints (1,-9, -2) and (7,-1,8). (a) Give an equation…

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Q: to prove thát thế answers 20. Parabolas with vertex and focus on the x-axis. 21. Parabolas with axis…

A: We have to Find the Differential Equation of the Family of Parabolas with vertex and focus on the…

Q: d the standard form of the equation of the circle, if the center of the circle of radius 3 lies on…

A: Here we have to find the standard equation of the circle if the center of the circle of radius 3…

Q: dentify the graph _____ A. hyperboloid of one sheet parallel to x-axis B. hyperboloid of 2 sheets…

A: answer is in next step. please give a like !!

Q: The lateral surface of a water bottle consists of a circular cylinder of radius 3 and height 6,…

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Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: what type of quadric surface is the following: y² - (z²/3) = 1 + (x²/12) write the equation of its…

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Q: Describe the graph of the equation. r = 5 costi - 19 sin rj+k O An ellipse in the planex = 1, center…

A: The graph of the given equation is ; r = 5 cost i - 19 sint j + k We have to choose the correct…

Q: Match the quadric surface with the a plausible equation for the graph by drawing an arrow from the…

A: The objective is to match the surface with equation for graph and then by its name.

Q: Find a parametric representation for the surface. The part of the hyperboloid 9x2 – 9y2 – z2 = 9…

A: Let u and v be two parameters for the given surface. Since the part of the surface lies in front of…

Q: Let A be the sphere having diameter with endpoints (1, –9, –2) and (7, –1, 8). (a) Give an equation…

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Q: State the type of the quadratic surface: ()' + ()° + z : 1 1. Hyperboloid of two sheets 2.…

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Q: vertex. A small hyperbolic reflector 90 ft above the vertex and with one focus that coincides

A: The hyperbola eq y2a2-x2b2=1 where b2=c2-a2 has center (0,0), vertices(0,±a) and foci(0,±c)The…

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(−1,…

A: Given, Centre =C(-1,5,4) And Radius , R=4