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What is the equation of the circle, with center (4, 2) and radius 5 units?

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Answer:

Explanation:

Let us begin by just getting the equation of the circle first.

(x - 4)^2 + ( y - 2)^2 = 5^2

(x - 4)^2 + ( y - 2)^2 = 25

Now I'm going to graph that equation and discuss it here.

  • I have graphed the second equation above.
  • Notice that the center is at (4,2) just as the question requested.
  • A second point was put at (4,7). That was to show you that the radius is 5 units.
  • You can calculate that it is 5 units by noticing that 7 - 2 = 5
  • So the distance from the center to (4,7) is 5 units which is the amount of the radius.
  • Notice that the numbers representing the center have been reversed in sign. That is always done for a circle. The center's coordinates are always the negative of the coordinates given. You will be told why later.
What is the equation of the circle, with center (4, 2) and radius 5 units?-example-1
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