Question

May someone help me please ? I don't really understand this, and I need it turned in.

Answer 1

9514 1404 393

Answer:

  x^2 +y^2 +6x -18y +65 = 0

Step-by-step explanation:

The short of it is that you're being asked to rewrite each of these standard-form equations into general form: f(x,y) = 0.

It can save you a little effort if you recall that the square of a binomial is ...

  (a +b)² = a² +2ab +b²

Otherwise, you would use the distributive property to get ...

  (a +b)(a +b) = a(a +b) +b(a +b)

   = a² +ab +ab +b²

   = a² +2ab +b²

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For the given equation, expanding the squares gives ...

  (x +3)² +(y -9)² = 5²

  (x² +6x +9) +(y² -18y +81) = 25 . . . . . expand the squares

  x^2 +y^2 +6x -18y +65 = 0 . . . . . . . . subtract 25; put in order of decreasing powers of the variables