Final answer:
To find the coordinates of the minimum point of the curve y - x² = 10x + 9, complete the square by adding the square of half the coefficient of x to both sides. The minimum point has coordinates (-5, 9).
Step-by-step explanation:
To find the coordinates of the minimum point of the curve, we need to complete the square for the equation y - x² = 10x + 9. First, move all terms to one side of the equation:
x² + 10x + (y - 9) = 0
Next, we can complete the square by adding the square of half the coefficient of x to both sides:
x² + 10x + 25 + (y - 9) = 25
(x + 5)² + (y - 9) = 25
Now, we have the equation in the form (x - h)² + (y - k) = r², where (h, k) represents the coordinates of the minimum point. Comparing the equation with the standard form, we can see that the minimum point has coordinates (-5, 9).
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