Given the ellipse $\frac{(x - 4)^{2}}{4} + \frac{(y - 3)^{2}}{36} = 1$

Find the center point:

List the vertices:

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The center of the ellipse is $(4, 3)$ and the vertices are $(2, 3), (6, 3), (4, - 3), (4, 9)$

Steps

Step 1 ：Given the ellipse equation $\frac{(x - 4)^{2}}{4} + \frac{(y - 3)^{2}}{36} = 1$

Step 2 ：The center of the ellipse is given by the coordinates (h, k) where h and k are the values in the equation. In this case, the center is (4, 3)

Step 3 ：The vertices of the ellipse are given by the points (h±a, k) and (h, k±b) where a and b are the square roots of the denominators in the equation. In this case, the vertices are (2,3), (6,3), (4,-3), (4,9)

Step 4 ：Final Answer: The center of the ellipse is $(4, 3)$ and the vertices are $(2, 3), (6, 3), (4, - 3), (4, 9)$

Given the ellipse (x−4)24+(y−3)236=1 Find the center point: List the vertices:

Answer

Popular Problems

Given the ellipse $\frac{(x - 4)^{2}}{4} + \frac{(y - 3)^{2}}{36} = 1$

Find the center point:

List the vertices: