8-92. Describe how you would evaluate i" where n could be any integer.
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Answer:
This is the same as writing (x-9)^2 + (x-12)^2 = 225
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Explanation:
Any circle equation fits the template of
The center is (9,12) which tells us the values of h and k in that exact order.
h = 9
k = 12
To find the radius r, we need to find the distance from the center (9,12) to a point on the circle. The only point we know on the circle is the origin (0,0).
Apply the distance formula to find the distance from (9,12) to (0,0)
The distance from (9,12) to (0,0) is 15 units. Therefore, r = 15
An alternative to finding this r value is to apply the pythagorean theorem. The distance formula is effectively a modified version of the pythagorean theorem.
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Since h = 9, k = 12 and r = 15, we can then say:
which is the equation of this circle.