The graph (x - 2)^2 + 3(y - 2)^2 = 25 is the graph of a(n) ________. Ellipse?
correct
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To determine the graph of the equation (x - 2)^2 + 3(y - 2)^2 = 25, we can analyze its form and properties. The equation is in standard form for an ellipse:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1,
where (h,k) represents the center of the ellipse, a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the vertices along the y-axis.
Comparing this standard form with the given equation, we can see that h = 2, k = 2, a = 5, and b = sqrt(25/3). Since the coefficient of the x^2 term (a^2) is positive and greater than the coefficient of the y^2 term (b^2), this denotes an ellipse.
Therefore, the graph (x - 2)^2 + 3(y - 2)^2 = 25 represents an ellipse.