Find the equation of an ellipse with minor axis length 8 and vertices at (-9,3),(7,3)
is this right so far? (X+1)^2/not sure +(y-3)^2/64=1
The length of the minor axis is 8, so use (8/2)^2 as the denominator for the minor term.
... (y-3)^2 / 16 ...
The length of the major axis is 7-(-9)=16.
8m=$36.00
To find the equation of an ellipse, we need the coordinates of the center and the lengths of the major and minor axes.
Given that the minor axis length is 8, the endpoints of the minor axis are (-9, 3) and (7, 3). Since the center of the ellipse lies on the minor axis, it will have the same y-coordinate as the endpoints, which is 3.
The center of the ellipse is the midpoint of the minor axis, so the x-coordinate of the center can be found by taking the average of the x-coordinates of the endpoints:
center_x = (-9 + 7)/2 = -1/2
Now that we have the coordinates of the center, we can write the equation of the ellipse in standard form:
(x - center_x)^2/a^2 + (y - center_y)^2/b^2 = 1
where a is the length of the semi-major axis, and b is the length of the semi-minor axis.
Since the minor axis length is given as 8, the semi-minor axis length (b) is 8/2 = 4.
Plugging in the values, we get:
(x - (-1/2))^2/a^2 + (y - 3)^2/4^2 = 1
(x + 1/2)^2/a^2 + (y - 3)^2/16 = 1
The equation of the ellipse is:
(x + 1/2)^2/a^2 + (y - 3)^2/16 = 1