Given the ellipse find the coordinates of its center and vertices 25x^2+9y^2=225
To find the center of the ellipse, we first need to rewrite the equation in standard form by dividing each term by 225:
x^2/9 + y^2/25 = 1
Now we can identify the center of the ellipse to be (0,0) since it is centered at the origin.
To find the vertices of the ellipse, we can identify the major and minor axes. The major axis is along the x-axis and has a length of 2a, where a is the square root of the larger number in the denominator of the standard form equation. In this case, a = √25 = 5.
The minor axis is along the y-axis and has a length of 2b, where b is the square root of the smaller number in the denominator of the standard form equation. In this case, b = √9 = 3.
The vertices are located along the major axis, so we can find the coordinates of the vertices by adding and subtracting a from the x-coordinate of the center. Therefore, the vertices of the ellipse are (5,0) and (-5,0).