Find the dimensions of the rectangle with maximum area that can be in- bed in the ellipse x²/a² + y² /b² = 1.

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Q: write the equation of the ellipse 9x2+36y2+90x+216y+225= 0 in standard form, please show all written…

A: Standard equation of ellipse is x-x02a2+y-y02b2=1    when major axis on the horizontal axis

Q: Find the points on the ellipse  X^2 + 6y^2 + 3xy =40 With the greatest x coordinator

A: Let us assume thatfx,y=xandgx,y=x2+6y2+3xy-40The lagrange multiplier equations…

Q: Write an equation of the ellipse in standard form ((x-h)/a)^2 + ((y-k)/b)^2 =1

A: Standard form of ellipse isx-h2a2+y-k2b2=1

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…

Q: Sketch a graph of the ellipse 9x^2+2y-54x+y^2+46=0 and determine the coordinated of the foci, the…

A: Given, This an equation of an ellipse.

Q: Find the area of the largest rectangle that can be inscribed in the ellipse 1.

A: To find the area of the largest rectangle