Question

given the ellipse \frac{(x-4)^2}{36} + \frac{(y-2)^2}{9} = 1

find the center point:

list the two major vertices (separated by a comma):

Explanation:

Step1: Identify the standard equation form

$$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$

Step2: Determine the center point

$$(h, k) = (4, 2)$$

Step3: Find the semi-major axis length

$$a = \sqrt{36} = 6$$

Step4: Calculate the major vertices

$$(h \pm a, k) = (4 \pm 6, 2) = (-2, 2), (10, 2)$$

Answer:

Center point: \((4, 2)\)
Major vertices: \((-2, 2), (10, 2)\)