How do you write 25y^2 + 9x^2 - 50y - 54x = 119 in standard form?

1 Answer
Alan P.
May 3, 2015

25y^2+9x^2-50y-54x = 119

Consider the tow sub-expressions from the left side of this equation:

  1. Terms involving color(red)(y)
    color(red)(25y^2-50y)
    color(red)(= 25(y^2-2y))
    color(red)(=25(y^2-2y+1) -25)
    color(red)(=5^2(y-1)^2 -25)

  2. Terms involving color(blue)(x)
    color(blue)(9x^2-54x)
    color(blue)(=9(x^2-6x+(-3)^2) -81)
    color(blue)(=3^2(x-3)^2 -81)

25y^2+9x^2-50y-54x = 119
25y^2-50y +9x^2-54x = 119
=color(red)(5^2(y-1)^2 -25) + color(blue)(3^2(x-3)^2-81) = 119
=5^2(y-1)^2+3^2(x-3)^2 = 225
or
=(25y-25)^2+(9x-27)^2= 15^2
or
some variant of this depending upon your local definition of "standard form" for an ellipse.

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