Match each equation to the appropriate graph and classify (name) the quadric surface. c. -x2 – y? + 22 = 1 d. 22 = x² + y² a. 4x2 + y? + 2² = 4 e. 4x? + 9y² – 36z² = 36 %3D b. 2 = 4x? + y² f. z = y² – x² Equation: |Name of Quadric Surface: Equation: Equation: Name of Quadric Surface: Name of Quadric Surface: Equation: Equation: Equation: |Name of Quadric Surface: Name of Quadric Surface: |Name of Quadric Surface:

Q: Choose the equation that represents the graph of the quadric surface below 3. 21 O z = 4 - 5y2-92 O=…

A: From graph we see that the quadric surface represents a paraboloid whose axis is y-axis Here 1st…

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

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Q: 5. Which equation represents the parabola with focus (1, 4) and latus rectum of 4? O y = (# – 1)2 +…

A: y= (1/4) *(x-1)^2 +3

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: 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: 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: name the surface represented by the equation r^2+z^2=4-2z

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Q: Describe in words the surface whose equation is given. p = 5

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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: a) makes horizontal traces, shows the development and graph b) make three vertical traces, show the…

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

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Q: 6. What is the equation for the slope of the ellipse+= 1 at (x₁, yi)? A. B. C. D. E. y' = y' = b²y₁…

A: We have to find the equation of the slope of ellipse at the point (x1,y1).

Q: Determine the equation of the parabola with the directrix z = 3 and focus (0, 7). O y = 8 (z – 5) O…

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

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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: x² + + =1 y2 9. 4

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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: The hill has the shape of a cone, which in the XYZ system has the equation z = 4 - sqrt(x^2+y^2) A…

A: Given that hill has the shape of the cone given by z=4-x2+y2 and the tourist moves uphill whose path…

Q: 3. Write an equation for the parabola with focus (1, 3) and vertex (0, 3). a. y = 4(x – 3)² b. y =…

A: Given:      focus =1,3      vertex =0,3  The focus and vertex are horizontally aligned, so the…

Q: What are the distances from the point (x, y) to the focus of the parabola and the directrix? Select…

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

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Q: Find equations for two lines through the origin that are tangent to the ellipse a- 8x +y + 3 =0.

A: We are asked to find the equation of two lines that are tangent to the ellipse.

Q: Describe in words the surface whose equation is given. p = 7 O a circular cylinder with radius 7 and…

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Q: • Consider the surface given by the equation (r- 1)² + (y+3)2 - (z-2)² = 1. Which of the following…

A: We have to find y- intercept.

Q: Homer wants to identify the center and radius of the circle defined by the equation x² + y² – 14x +…

A: He failed to add the new constant terms to both sides of the equation.

Q: Write the equation for the above surface.

A: The surface represents the cylinder; with circle in the xz-plane. x2 + z2 = 1  (radius of the circle…

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: For the sphere with equation (x - 1) + (y + 2) + (z + 4) = 36, find a) the center. b) the length of…

A: The given sphere equation is x-12+y+22+z+42=36.

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

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Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

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Q: Assume the equation of a parabola and a line are given by y = x +2 x and y =3 x +6, respectively.…

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

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Q: Choose the equation that represents the graph of the quadric surface below 3 O y = 4 – 5x² – 922 O I…

A: We have given a quadric surface. It is asked to find the equation of the surface from the given…

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: 4a. x +4y? +9z? = 36 Name of the surface Y

A: Given:  x2+4y2+9z2=36

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: 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: 1. Determine the equation of a circle with the center at origin and a radius of 6 units? y2 35 c. x2…

A: 1) Given:      Radius r=6 units. Equation of circle with center at origin is               x2+y2=r2…

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: Write the equation and determine the type of surface obtained by rotating this line around the…

A: When we rotate the given equation around y axis, we got hyperboloid:

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

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

A: Question is solved.

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

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.

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.