1. Describe the graph of x² +y? +(z-7) = 49 2. Give the equation of the above graph BOTH in spherical and in cylindrical coordinates.

Q: Match the surface to its corresponding equation in spherical coordinates. 4 2 3 4. %3D 2 1 а. -1 -2…

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Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: 7. (a) Find a spherical coordinate equations; for the sphere x²+y²+(z-1)²=1 and the surface…

A: To convert a point from Cartesian coordinates to spherical coordinates, use equations…

Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: →cos(nπ) = (-1)n  →First find the inital co-ordinates at t = 0. Now, we have to find the time at…

Q: x + xy + y? = 9 %3D sa slanted ellipse illustrated in this figure: 1 – 4 -2 2.

A: Given that x2+xy+y2=9 Differentiate w.r.t x , 2x+y+xy'+2yy'=0 y'=-2x+yx+2y Now, differentiate w.r.t.…

Q: 42. Hyperbola: = h+a sec 0, y= k+b tan 0

A: Use trigonometric function: 1+tan^2(theta) = sec^2(theta)

Q: Convert the given equation, -z2- y2 +=1, z20 to an equation in cylindrical coordinates.

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Q: 8. Give a parametric representation of the given ellipse with the orientation clockwise. x2 y? -=D1…

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Q: Match each equation with a description of the shape of its surface. 2 A. hyperbolic paraboloid B.…

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Q: 4. Consider the ellipse given by the equation y? x + 1. 9. Find the curvature of the ellipse at the…

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Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: and an equation in cylindrical coordinates for the equatic = 25x²+25y²-2

A: topic:- coordinate system

Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

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Q: = 1 10 12 = 1 20 12 x2 = 1 100 36 =1 100 144

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Q: Determine the shape of each polar curve. 9r = 7 parabola 7 circle 9 r = 4 + 6 sin(0) ellipse…

A: Given :            r=7r=74+6sinθr=74+4sinθr=76+4sinθ

Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

Q: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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

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Q: Given the equation of an ellipse in parametric form:x=acost,y=bsint,where a, b are semi-axes of the…

A: Equation of ellipse in parametric form is Differentiating with respect to t, we get Now,

Q: 4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this ellipse, find: 1. the ones…

A: 1. Note that the smallest and largest value of y occur when dy/dx =0. Taking derivative on both…

Q: 2. Find the point(s) of intersection of the following two parametric curves, by first eliminating…

A: From x=t+5 we get t=x-5 Then we plug this in the y=t2 So, the equation is: y=(x-5)2   We can plug…

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: Consider a particle traveling clockwise on the elliptical path                              x2/ 100…

A: Given: x2100+y225=1  or  x2102+y252=1 Leaving point of the particle from the orbit (−8,3)

Q: Find the spherical equation for the hyperboloid of two sheets x² – y² – 2² = 1.

A: Given information :  Equation of hyperboloid of two sheets x2-y2-z2 = 1

Q: find an equation of the form ρ = f (θ , φ) in spherical coordinates for the following surfaces  x2…

A: Solution:- x2-y2=4 x=ρ sinφ cosθ y=ρ sinφ sinθ   ρ sinφ cosθ2-ρ sinφ sinθ2=4 ρ2 sin2φ cos2θ-ρ2 sin2φ…

Q: Match the ellipsoids shown in the table with the equations. Answer Bank x2 + 2y2 + 2z² = 4 2x2 + 2y?…

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Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

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Q: The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid

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Q: A lizard moves through the plane with its position at t seconds given by the parametric equations…

A: parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1.

Q: Try to sketch by hand the curve of intersection of the circu- lar cylinder x + y² = 4 and the…

A: Given, Circular cylinder, x2+y2=4 Parabolic cylinder, z=x2

Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

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Q: Find the eccentricity of a hyperbola whose transverse axis and conjugate axis are equal in length O…

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Q: Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. e =…

A: Solution:

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

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Q: 17. Evaluate F · dš if F(x, y) = (y*, 2xy*) and & is the ellipse x? + 2y? = 2 (with counterclockwise…

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Q: Consider the equation of an ellipse written in terms of x and y as 13 z? + 8 yz + 7 y² = 1 a. Find…

A: Note:- For a non singular square matrix A,  A = PT D P  Here, P is orthogonal matrix that is, P-1 =…

Q: 1. Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find a corresponding…

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Q: The ellipse x^2/7^2 + y^2/6^2 = 1can be drawn with parametric equations where x(t) is written in the…

A: x272+y262=1since 7&gt;6 S0 major axis on x-axis

Q: Choose the equation that represents the graph of the cylindrical surface below O2 + y? = 1, = 5 O…

A: We have plotted the graph:- second option

Q: The equation z = 1+r² in cylindrical coordinates represents Select one: O a paraboloid O a circle O…

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Q: 1 in (r', y')-coordinates, if (iii) Find the equation for the hyperbola ry 0 = 1-

A: Find the equation of hyperbola in x'y' system

Q: Match the following equations with appropriate ones. 물 %3 11 Ses- Seç. Seç. Seç. Seç. Hyperbolic…

A: Solutions We have to match each equation as in options

Q: (41, Ellipse:. x = h + a cos 0, y= k + b sin 8

A: Form ellipse

Q: Match the equation (written in terms of cylindrical or spherical coordinates)  = 5, with its graph.

A: Solution: Consider the general equation of the sphere is x-a2+y-b2+z-c2=r2 we have a relationship…

Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. hyperbola: x = h…

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Q: Find the cylindrical equation for the ellipsoid 4x2 + 4y² + 2² = 1.

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Q: Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0…

A: Given equation of the ellipse 9x2+4y2+24y=0.

Q: What is the Cartesian form of the parametric equations æ(t) = 4cost – 1 and y(t) = 5sint + 2?…

A: Here I am attaching image so that you understand each and every step.