Question

Graph the circle which is centered at (-4,1) and which has the point (0,4) on it

Answer 1

Answer:

  see the attachment for the graph

Step-by-step explanation:

Since all you want is the graph, it is convenient to use a graphing program to produce it.

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You will notice that the point on the circle is 4 units over and 3 units up from the center.* This tells you the square of the radius is 4²+3² = 25. You only need to know this if you're using a graphing calculator to plot the equation ...

  (x +4)^2 +(y -1)^2 = 25

If you're graphing this by hand, you can set your compass to the distance between the plotted points, as we have done in our graphing program.

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* Hopefully, you recognize these (4 and 3) as the legs of a 3-4-5 right triangle, so you know immediately that the radius is 5. Even if you don't, you can figure it using the Pythagorean theorem, as we have done above.

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The standard form equation of a circle with center (h, k) and radius r is ...

  (x -h)^2 +(y -k)^2 = r^2