x, y From a variable point of an ellipse - + 2 = Inormal is drawn to the ellipse. %3D a' b? Find the maximum distance of the normal from the centre of the ellipse.

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

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Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: a. Find the area of the surface generated by revolving about the x-axis the loop of the

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Q: when curve y=arctan(x) is revolved about the y-axis, give the equation of the surface of revolution.

A: To find the equation of the surface of revolution

Q: Find the area of the surface of revolution generated by revolving the curve y = 5/ 0Sa<4, about the…

A: Given that:  y=5x,                        0≤x≤4

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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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…

A: Given

Q: The arc of the parabola y = 5x2 from (5, 125) to (15, 1125) is rotated about the y-axis. Find the…

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Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: Keparametrize the curve rit) = with respect to its arclength measured from the point (e"20,e"2) in…

A: Given curver(t)=etsint,etcost,et Above curve is passes from the point eπ2,0,eπ2.we need to find the…

Q: radiation is focused to an unhealthy area in a patient’s body using a semi elliptical reflector,…

A: Given that width of the reflector=100cm          And height of the reflector=30cm Here the foci lie…

Q: A space agency's large parabolic dish had a diameter of 12 feet, with a focal length (the distance…

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Q: Consider the ellipse described by x = cost, y= 3sint for te [0,2x]. Construct an integral whose…

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Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Find the area of the surface obtained by rotating the parabola 1 y = 0 <x < 2, about the y-axis.

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Q: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: The line y = mx +b intersects the parabola y = x^2 at points A and B. Find the coordinates of the…

A: The line y=mx+b intersects the parabola y=x2 at the pointsA and B.Let A=x1,x12 and B=x2,x22, where…

Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: Use the parametric equations of an ellipse x = 10 cos 0 y = 22 sin 0 0 ≤ 0≤2T to find the area that…

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Q: The area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: Area of ellipse initially  = Ai  = πab    Now, lengths of axis are changed,   They are  [ 2(1.0099)a…

Q: Find on equation of the porabola with focus at F (0,-1) and directrix :y=1 in standerd form

A: Find an equation of the parabola in standard form with focus at F (0-1) and directrix : y = 1

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

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Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: The ellipsoid 4x² +2y² + z² arametric equations for the tangent. line to this ellipse at th = 16…

A: The given equation of ellipsoid is 4x2+2y2+z2=16 intersects the plane y=2 in an ellipse. Let…

Q: Find the area of the surface generated by revolving the given curve about the y- axis. x=2₁√√6-y,…

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Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: Radiation is focused on an unhealthy area in a patient’s body using a semielliptical reflector,…

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Q: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

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Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 8t, y - 6t…

A: Given that, x = 8t y = 6t + 1 0≤t≤1 We have to find the area of surface generated by revolving the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y =

A: Given curve is  y=x36+12x Differentiate with respect to x. dydx=x22-12x2

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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Q: Find the area of the surface obtained by rotating the curve about the x-axis. Recall: S=2n |…

A: Find the surface area

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

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Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

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Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

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Q: Find the surface area of the ellipsoid obtained by rotating the ellipse (=) = 1 about the x-axis.

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Q: ltermine the surface arca of the solid obtained by rotating y= 19- XZ about the X- axis.

A: Given:- y = √(9-x^2).  To find:- Surface area of solid obtained by rotating about the x axis [-2, 2]…

Q: Find the exact area of the surface obtained by rotating the curve about the xx-axis.  y=sin(πx/8),…

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Q: The curve y = V4-x², -1<x<1, is an arc of the circle x2 + y² = 4. Find the area of the surface…

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Q: 2. y = ln(x²-1), 2 ≤ x ≤ 3 ;y-axis

A: The given problem is to find the area of surface of the revolution of the given curve over the given…

Q: 1. a. Draw the ellipse x + y/4 1 and label its x and y intecepts. b. View the ellipse as a type I…

A: type i regions are bound by vertical lines (i.e. x=a) where as type ii regions are bound by…