Find the points on the ellipse 3x + y = 3 that are farthest away from the point (1, 0). smaller y-value (x, y) = %3D larger y-value (x, y) = %3D

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

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: he plane r+y+ 2z 10 intersects the paraboloid z = x + y in an ellipse. Find the points on this…

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Q: The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. Find the points on the ellipse…

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Q: Find center, foci , vertices, asymptotes and radious of 2x? + 2y² – 28x + 12y + 114 = 0

A: Given: 2x2+2y2-28x+12y+114 = 0

Q: The plane x+ y+2z =2 intersects the paraboloid z = x2+y² in an ellipse. Find the points on this…

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Q: Find the point(s) on the hyperbola y^2 − x^2 = 4 that is (are) close to the point (2, 0

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Q: Find an equation of the normal line to the ellipse x2/32 + y2/8 = 1 at the point (4, 2). (a) Use a…

A: Proceed as below to find the equation of normal.

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

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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: The plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. Find the points on…

A: Given the plane x + y + 2z = 30 intersects the paraboloid z = x^2 + y^2 in an ellipse. We need to…

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: 5(c) Find the rectangle with the largest area that can be inscribed in the top half of the ellipse ²…

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Q: The plane x + y + 2z = 12 intersects the paraboloid z = x² + y2 in an ellipse. Find the points on…

A: Suppose the point nearest to origin with the condition that it is not the ellipse that is obtained…

Q: find a parametrization for the curve. the upper half of the parabola  x-9=y^2

A: The given curve is x-9 = y2  ...(a) Putting y = t in (a) then x = 9+ y2…

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: Find a normal of slope 2/3 to the hyperbola 3x2-4y2=8

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Q: Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0).   smaller…

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Q: Find the maximum and minimum values of f(x, y) = 5x + y on the ellipse x² + 16y² =1 maximum value:…

A: Given: fx,y=5x+y. Ellipse x2+16y2=1. To find: The maximum and minimum value of f subject to the…

Q: 3) A large racetrack can be modeled by the ellipse x2 + = 1, where x and y are measured in…

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

A:

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: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/22^2 + y^2/10^2 = 1. The…

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Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 using Lagrange…

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

A: Area of the ellipse = πab.

Q: Use the method of Lagrange multiplier to find the largest and least values of h(x, y) = x²y on the…

A: We need to use Lagrange multiplier to solve this problem. h(x, y) = x²y x² + 2y² = 6

Q: Find the maximum and minimum values of f(x, y) = 4x + y on the ellipse a² + 36y² = 1 %3D maximum…

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Q: Prove that evolute of the ellipsé x2 y? = 1 a? b2 is (ax)2/3 +(by)2/3 = (a² – b²)²/3. %3D

A: Given equation of the ellipse be x2/a2 + y2/b2 = 1 Write the equation of the ellipse in parametric…

Q: .... .. ......... ....*.*. ..* * ..... The area of an ellipse with axes of length 2a and 2b is nab.…

A: As per our guidelines , we can only solve first question. Please resubmit other questions as next…

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

A:

Q: 2. The plane r + y +2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

A: According to the given information, it is required to find the nearest and farthest distance from…

Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

A:

Q: 4. The base is the ellipse 4> cross section is a semici the x-axis.

A: Given ellipse equation is  4x2+y2=1 Solve for y y2=1-4x2Take square root on both sidesy=1-4x2 The…

Q: help with a, b and c please

A: We have to find the points on the ellipse that are farthest from point (1,0).

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 maximum and minimum values of f(x, y) = 3x + y on the ellipse x? + 16 = 1 maximum value:…

A:

Q: The plane x + y + 2z = 6 intersects the paraboloid z = x2 + y² in an ellipse. Find the points on…

A: To find the farthest and nearest point from the origin to the ellipse.

Q: A space probe in the shape of the ellipsoid 4x + y +4z = 16 enters the earth's atmosphere and its…

A: To determine the hottest and coldest points on the probe's surface.

Q: The cylinder x² + y² an ellipse. Find the points on that ellipse that are closest and farthest from…

A: The cylinder x2+y2=1 intersects the plane x+z=1 in an ellipse. We need to find the points on the…

Q: A rectangle of maximum perimeter is to be inscribed in the ellipse x^2/20^2 +y^2/11^2=1. The…

A: Explained below

Q: (a) Where does the normal line to the ellipse x - xy + y²-3 at the point (-1, 1) intersect the…

A: To find next coordinate points of normal line to ellipse, find the derivative of given equation of…

Q: H.W: Find the center of mass- a thin Plate af deusity S=3 bouuded the by lines X- o, y=x iad the…

A: we have to find the center of the mass of a thin plate of density δ =3 bounded by the line x=0, y =…

Q: Find the maximum and minimum values of f(x, y) maximum value = = xy on the ellipse 2r2 + y? = 2.…

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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:

A:

Q: The plane x + y + 2z = 20 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

A: