Write an equation of a circle with its center (14, 17) and point on a circle (15, 17).Question 6Select one:a.(x − 14)2 + (y − 17)2 = -1b.(x − 14)2 + (y − 17)2 = 1c.(x + 14)2 + (y + 17)2 = 1d.(x − 14)2 + (y + 17)2 = 1
Question
Write an equation of a circle with its center (14, 17) and point on a circle (15, 17).Question 6Select one:a.(x − 14)2 + (y − 17)2 = -1b.(x − 14)2 + (y − 17)2 = 1c.(x + 14)2 + (y + 17)2 = 1d.(x − 14)2 + (y + 17)2 = 1
Solution
The equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Given the center of the circle is (14, 17) and a point on the circle is (15, 17), we can find the radius by calculating the distance between these two points.
The distance between two points (x1, y1) and (x2, y2) is given by √[(x2 - x1)² + (y2 - y1)²].
So, the radius r = √[(15 - 14)² + (17 - 17)²] = √[(1)² + (0)²] = √1 = 1.
Substituting h = 14, k = 17, and r = 1 into the equation of the circle, we get:
(x - 14)² + (y - 17)² = 1²
So, the equation of the circle is (x - 14)² + (y - 17)² = 1.
Therefore, the correct answer is b. (x - 14)² + (y - 17)² = 1.
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