Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the xy-trace of the sphere.

Q: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

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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 largest and smallest values that the function ƒ(x, y) = xy takes on the ellipse x2/8 + y2/2…

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Q: 2 Q2 Given the following conic section, determine its shape and then sketch its graph. a - V3ry + 2y…

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Q: Find the equation of tangent lines to the ellipse parallel to the line y =3. The equation of ellipse…

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

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Q: Find the maximum and minimum values of the function f(, y) = xy on the ellipse given y? by the…

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Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25 Sketch…

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Q: Find the equation for a hyperbola centered at (0, 0), with foci at (0, - V 52 -6) and (0, 6). y? x2…

A: Here we have to find the equation of hyperbola having a center (0,0) with foci at 0,-52 and 0,52 and…

Q: h) Find a parametric representation of the Parabolic equation z = 9(x² + y²)

A: Parametric representation of the Parabolic equation z = 9(x² + y²) will be cartesian coordinates as…

Q: z' +z+1 Evaluate -dz , where C is the ellipse 4x + 9y = 1. c z² – 3z+2

A: By Cauchy integral theorem,            If the function fz in analytic in some simply connected…

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

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

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

Q: Q.9: Classify and find the standard equation of the conic section 4x² +9y² + 36y-16x + 16 = 0, then…

A: Given

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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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: 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 parabola y=x^2+13 has it's focus at the point (b,c) where  b= c=

A: The given equation of the parabola is, y = x2+13. Also the parabola has its focus at (b, c).Consider…

Q: 2 Write the equation of the hyperbola – 25 · x? + 16 · y² = 400 in standard form + = 1 %3D

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Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: Use the Discriminant Test to determine the type of the conic section (in each case, the equation is…

A: To determine the type of conic section

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 evolute of the parabola y=x2.

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Q: (e) x = 4 – z²

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

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: 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: What is the directrix of the parabola? (z+3) =8 (y-1) O y= 3 O y=2 O y= 1 o y=-1

A: If General equation of parabola :  y = a ( x - h ) 2 + k  Then directrix y = k - ( 1/4a )

Q: C'enter of the hyperbola x? + 4y? + 6xy + 8x 2y + 7 = 0 is - A. (1, 1) В. (0, 2) С. (2,0) D. None of…

A: Given: x2+4y2+6xy+8x-2y+7=0 To Find: Center of Hyperbola Concept: Let the equation of the hyperbola…

Q: H. Identify the conic sections represented by the following formula a) 2x2 – 8xy + 4x = 12 b) x² + y…

A: I have solved first 3parts only and for all parts solution repost again

Q: 1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open? *

A: We have to find the direction in which the given parabola opens.

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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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: A surface in space is defined by the equation -4x? + 16y- 8z2 = 0. Which one of these is true? O The…

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Q: Classify and sketch the surface 12x? – 3y? + 4z? = 12 What are the 3 traces? Show equations of the…

A: A quadratic surface is a hypersurface. It is nothing but the generalization of a conic section in…

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: The figure below shows a lamp located three units to the right of the y-axis and a shadow created by…

A: Here we need to calculate equation of tangent line on given ellipse which passes through (-5,0)  If…

Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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

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Q: 2. Find the equation of the parabola with focus (2, 0) and directrix x = -2. а. b. x' = 8y c. y = 8x…

A: Since you have asked multiple questions according to our company guidelines we are supposed to…

Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: Consider the Equation:  x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0 1. Show that the equation represents…

A: x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0

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: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: use the Discriminant Test to determine the type of the conic section (in each case, theequation is…

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Q: Which conic section is represented by the equation 9x2+4y2=36

A: Simple conic section problem......