Question

decide whether or not the equation below has a circle as its graph.

49x^2+49y^2-56x+56y-49

Answer 1

do you know the equation of a circle?

Answer 2

(x-h)^2 + (y-k)^2 = r^2

Answer 3

There's another form: the general one.\[\rm x^2 + y^2 +Cx + Dy + E = 0\]

Answer 4

Is the equation in your question in general form?

Answer 5

yeah

Answer 6

Well, do a thing... let's divide each term by 7.

Answer 7

\[\rm 49x^2 -56x + 49y^2 - 56y = 49\]so,\[\rm 7x^2 - 8x + 7y^2 - 8y = 7\]factoring,\[\rm x(7x - 8) + y(7y - 8) = 7\]Hmm we already know that this ain't a circle