Which of the following is a result of shifting a circle with equation(x + 3)2 + (y - 2)2 = 36 up 3 units?A.Both the x- and y-coordinates of the center of the circle increase by 3.B.The y-coordinate of the center of the circle increases by 3.C.The y-coordinate of the center of the circle decreases by 3.D.The x-coordinate of the center of the circle increases by 3
Question
Which of the following is a result of shifting a circle with equation(x + 3)2 + (y - 2)2 = 36 up 3 units?A.Both the x- and y-coordinates of the center of the circle increase by 3.B.The y-coordinate of the center of the circle increases by 3.C.The y-coordinate of the center of the circle decreases by 3.D.The x-coordinate of the center of the circle increases by 3
Solution
The equation of a circle in a coordinate plane is given by (x - h)² + (y - k)² = r², where (h, k) are the coordinates of the center of the circle and r is the radius.
In the given equation, (x + 3)² + (y - 2)² = 36, the center of the circle is at (-3, 2).
If we shift the circle up by 3 units, it means we are increasing the y-coordinate of the center by 3. So, the new center of the circle will be at (-3, 2+3) = (-3, 5).
Therefore, the correct answer is B. The y-coordinate of the center of the circle increases by 3.
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