Equation of a Circle | MathHelp.com
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Here we’re asked to write the equation of a circle with center (-2, 7) and radius 5. Remember from the previous example that the formula for the equation of a circle is (x – h)^2 + (y – k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius. And in this problem, since we’re given that the center is (-2, 7), which represents (h, k), and radius is 5, which represents r, we simply plug these values into the formula. And we have x – parentheses -2 squared….+ y – parentheses -7 squared…= parentheses 5 squared. Notice that I changed the parentheses that were in the original formula to brackets so that we wouldn’t have too many sets of parentheses when plugging our values into the formula. Finally, we simplify inside the brackets. x minus a negative 2 simplifies to x + 2, so we have parentheses x plus 2 squared + parentheses y – 7 squared = 5 squared, or 25. Notice that I changed the brackets back to parentheses in the final answer. So the equation of a circle with center (-2, 7) and radius 5 is (x plus 2)^2 + (y minus 7)^2 = 25. Notice that the negative 2, positive 7 in our given center becomes a positive 2, negative 7 in our formula, and don’t forget to square the radius of 5 to get 25.
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