Which of the following is a result of shifting a circle with equation(x + 3)2 + (y - 2)2 = 36 up 3 units?

Question

$(x + 3)^2 + (y - 2)^2 = 36$
up 3 units?

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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.

In the given equation, (x + 3)² + (y - 2)² = 36, the center of the circle is at (-3, 2) and the radius is √36 = 6.

If we shift the circle up by 3 units, the y-coordinate of the center will increase by 3. So, the new center will be (-3, 2 + 3) = (-3, 5).

Therefore, the equation of the shifted circle will be (x + 3)² + (y - 5)² = 36.

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