Find the area (in units2) enclosed by the ellipse x2 16 +  y2 25 = 1

Q: Find the points on the ellipse x2+2y2=1, where f(x,y)=xy has its extreme values.

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Q: Find the surface area of the object obtained by rotating y = 1 +. 8x2 , 2<x 3 about the x-axis. 4

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Q: Given an ellipse with major axis of length 2a and minor axis of length 2b, the area is given by A =…

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Q: Let a &gt; 0 and b &gt; 0. Show that the area of the ellipse x2/ a2 + y2/ b2 = 1 is ab

A: Given that, The equation of the ellipse  x2/ a2 + y2/ b2 = 1 , where a &gt; 0 and b &gt; 0. Solve…

Q: Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes,…

A: Let 2x and 2y be the length and width of rectangle with sides parallel to the coordinate axes, that…

Q: Use the paramteric eauations of an ellipse, x=acos(theta), y=bsin(theta), 0<=theta<=2*pi, to find…

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Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: Rotate the ellipse =1 around the x -axis to approximate the volume of a football, as seen here.

A: To determine the volume of  that rotated about the x-axis. Given, The given curve is ellipse.…

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

A: We have to find percent change in the area after increasing major axis and minor axis.

Q: What is the area of the conic (x + 3) + y 25

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Q: find the exact perimeter of the ellipse x2/a2 + y2/b2 = 1. (No approximations) please show all the…

A: Consider the provided question,

Q: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: What is the highest point on the ellipse that is the intersection of the plane x + y + 2z = 2 and…

A: Given  the intersection of the plane x+y+2z=2 and the paraboloid z=x2+y2

Q: Find the area of the surface obtained by revolving the graph of y = √x(4x − 3)/6, 1 ≤ x ≤ 9 about…

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Q: Q.2. Show that the area of the ellipse =1 is z ab. ab

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Q: The plane 6x + 8y + 60z = 700 intersects the cone z = x + y in an ellipse. The sum of the z-…

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Q: || 9x2 dA, where R is the region bounded by the ellipse 9x2 + 25y2 = 225; x = 5u, y = 3v

A: Here we use transformation to solve this problem.

Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

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Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: Find the area inside the ellipse x2a2+y2b2=1.

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

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Q: Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller…

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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: Find the area enclosed by the ellipse x2/a2 + y2/ b2 = 1 shown in the figure.

A: Consider the following equation of ellipse: x2a2+y2b2=1y2b2=1-x2a2yb=a2-x2a2y=baa2-x2

Q: 4. Find the area of the largest isosceles triangle that can be inscribed in the ellipse y2 = l. a2…

A: To find the area of the largest isosceles triangle.

Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

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Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: Find the volume of the ellipsoid x2a2+y2b2 +z2c2 =1.

A: Volume of the solid in region R is, V=∫∫∫RdV We know that spherical coordinate of ellipsoid is,…

Q: Evaluate [xydxdy where D is the region D in the first quadrant of the ellipse 9x +4y = 36 in the…

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: What is the area of the ellipse x² 16 + y² 9 = 1?

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Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: Assume the equation for an ellipse is Ax +2Bxy + Cy D where D has the units of area. Show, by…

A: Given that Ax2+2Bxy+Cy2=D is an ellipse, where D has the units of area. To prove that the area of…

Q: Find the maximum and minimum values of f(x, y) = 7x + y on the ellipse x2 + 9y² = 1

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Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: Find the centroid of the lamina cut by the parabolas y2=x and y=x2.

A: For the clear understanding of curve we have the following graph which is shown below as:

Q: x, y From a variable point of an ellipse - + 2 = Inormal is drawn to the ellipse. %3D a' b? Find the…

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Q: Find the volume of the solid formed if we rotate the ellipse+ = 1 about the line 4x + 3y = 20.

A: Calculation of Volume.

Q: Find the maximum and minimum values of f(x, y) 3x+y on the ellipse +25 = 1 %3D maximum value:

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Q: 4x^2 + y^2 = 4 that are the farthest away from point (1,0)

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Q: Find the volume of the solid of revolution if a quarter of an ellipse in the first quadrant with…

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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 area enclosed by the ellipse (x2/a2) + (y2/b2) = 1

A: Consider the given equation as x2a2+y2b2=1

Q: The ellipse y? q? + = 1 x2 %3D a2 62 is rotated about the x-axis to form an ellipsoid. Find the…

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Q: Find the area enclosed by the ellipse x2  / a 2    +   y2   /b 2    =1

A: Given ellipse is The ellipse meet x-axis at points (-a,0) and (a,0) and y-axis at points (0,-b) and…

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…