QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# mine the equation of the circle graphed below.
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Answer
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Step 1: Identify the given information and key points in the circle.
(x-h)^2 + (y-k)^2 = r^2
The circle in the image is centered at the origin (0, 0) and passes through the point (3, 4). Since the circle is centered at the origin, its equation will be of the form: where (h, k) is the center of the circle, and r is the radius. In this case, h = 0, k = 0, and we need to find r.
Step 2: Find the radius r.
r = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
Since the circle passes through the point (3, 4), we can find the radius r by calculating the distance between the origin (0, 0) and the point (3, 4). The formula for calculating the distance between two points (x^1, y1) and (x^2, y2) is: Using this formula, we get:
Final Answer
The equation of the circle is x^2 + y^2 = 25.
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