Question

Use the equation x2+9=6x−y2−6y−9x2+9=6x−y2−6y−9 to answer the questions. A: What is the equation in standard form? B: Does the given equation represent a circle, a point, or an empty set? Select one answer choice for question A, and select one answer choice for question B.

Answer 1

Answer:

• (x -3)² +(y +3)² = 0
• a point: (3, -3)

Step-by-step explanation:

A. Rearranging to standard form, you get ...

  x^2 +9 = 6x −y^2 −6y −9

  x^2 -6x +y^2 +6y = -18

  (x^2 -6x +9) +(y^2 +6x +9) = -18 +9 +9

  (x -3)^2 +(y +3)^2 = 0

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B. This represents a circle centered at (3, -3) with radius zero: a point.