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The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*ab. For this ellipse, a+b=20.
a. write the area of the ellipse as a function of a.
b. Find the equation of the ellipse with an area of 264 square centimeters.
c. Complete the table and make a conjecture about the shape of the ellipse with a maximum area.
a 7 8 10 11 12 13 14

  • geometry -

    (a) The area of an ellipse is
    A = pi*a*b.
    In this case,
    A = pi * a * (20 - a)

    (b) Set A = 264 and solve for a. Than use a+b=20. to get b, Then write the equation

    (c) Complete the table using a+b=20. If a = 7, b = 13.

    See which combination of a and b gives you a maximum value of a*b, and therefore of the area. I suspect it will be a = b = 10

    This is work you should be able to do yourself.

  • geometry -

    what is <mnp=60 degrees

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