Consider the following equation of a quadric surface. a. Find the intercepts with the three coordinate axes, when they exist. b. Find the equations of the xy-, xz-, and yz-traces, when they exist. c. Identify and sketch a graph of the surface. y? + 225z 36 x2 - 9 = 0 25

Q: Identify the surface defined by the following equation. 25x? +y? = 4 The surface defined by the…

A: Answer

Q: Find the standard form of the equation of a parabola given the following conditions: a.) Directrix:…

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

A: Equation of ellipsoid

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: What is the equation of a parabola with focus at (2,6) and directrixx = 8? %3D O y - 12y + 12z – 24…

A: Equating distance from directrix to distance from focus gives equation of parabola.

Q: B1² – 12:² = 16: %3D

A: Given: 3y2-12z2=16x

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

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Q: Find the parametric form of (i) the circle x²+y² = p² (ii) the ellipse 2 y² =1 (ii) the straight…

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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: Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the…

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Q: EXAMPLE 2 Describe and sketch the surface in R3 represented by the equation y = 6x.

A: Given equation : y = 6x in R3

Q: A hyperboloid of one sheet is any surface that can be described with an equation of the form…

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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 quadratic surface and sketch the graph of r+y +- 4xyz = 1

A: The given equation is: x2+y2+z2-4xyz=1

Q: identify the surface defined by the equation and match it to the appropriate graph

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Q: 18. Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. show solution

A: It represents hyperboloid.

Q: Find the equation of the surface of revolution when the hyperbola (y^2 / 9) − (z^2 / 4) = 1 is…

A: Find the equation of the surface of revolution when the hyperbola (y^2 / 9) − (z^2 / 4) = 1 is…

Q: By first writing the equation in standard form, identify the traces of the surface given by the…

A: Given equation:                           x2+3y2-6y+z2+4z-3=0

Q: Identify the type of surface represented by the given equation.

A: Since we are given x25+y28-z22=1 -(i) and for finding the nature of surfacewe will solve for z.

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: Given 4x = 3y + 3z2 (a) Write the equation above in standard form. (b) Identify the surface. (c)…

A: As per the guidelines we are only supposed to answer three subparts , for next parts please ask…

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: Identify the surface of the equation, show solutions.   Choices: A. Elliptic Paraboloid B. Cone…

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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: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: 4² – y² +25:² = 100 %3D

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Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x -

A: Rewrite the equation as z2 in terms of x and y.

Q: Find the following points of intersection. The point(s) of intersection of the parabola y = x2 + 2…

A: Given equation of parabola is y=x2+2 and equation of line is y=x+4. We have to find point of…

Q: 1. " Identify the surfaces of the following equations by converting them into equations in the…

A: As per the company guidelines i am solving first question please resubmit the question for another…

Q: State whether the equation y = 3x² defines a hyperboloid of one sheet. an elliptic cone. a…

A: Answer is mentioned below

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

A: Given

Q: Identify the focus and directrix of the parabola: y = -4(x - 2)² - 3. f: (1, -4), d: y = 2 f: (2,…

A: If the equation of parabola is of the form x-h2=4py-k(i)  if p>0  then focus is h,k+p  and…

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

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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: Identify and sketch manually the graph of the quadric surface 25x² -25y² -9z²-150x + 200 = 0.

A: Solution :-

Q: Rewrite the given equation of a quadratic surface and identify the graph. 12y2 – 3z2 = 16x

A: equation of the hyperbolic paraboloid  A y2 - B z2 = 2 Cx

Q: Given 4x2 + 9z2 = 9,2 (a) Write the equation above in standard form. (b) Identify the surface. (c)…

A: We have to  write the equation in standard form, name the surface, find its axis, sketch the…

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a…

A: The objective is to Identify the quadric surface and sketch it's graph.

Q: Identify and sketch by hand the graph of the quadric surface 25r2 – 25y? – 9z2 – 150r + 200 = 0. You…

A: An equation is given                              25x2-25y2-9z2-150x+200=0We have to identigy and…

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

A:

Q: Consider the following equation of a quadric surface. 9x2 + 4y? + 4z? = a. Find the intercepts with…

A: Question is solved.

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: Describe and sketch the surface represented by the given equation.y=-2

A: Given equation : y=-2 The graph of the equation is given below:

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.

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a…

A: Let's find.

Q: The equation x +4y² = 4 in three-dimensional space is an equation of which surface? O Ellipse O…

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