Find an equation of the ellipse satisfying the given conditions.
Center at (-2,3) with major axis of length 8 and parallel to the y axis, minor axis of length 2.
I don't understand how you get the formula for this. some help please
you should know that an ellipse with center at (h,k) and axes 2a,2b is
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
so, plug in your data. The only tricky part is knowing which are a and b. Since the major axis is parallel to the y-axis, (y-k)^2/b^2 will have the larger denominator.
(x+2)^2/1 + (y-3)^2/16 = 1
To find the equation of an ellipse given its center, major axis length, minor axis length, and orientation, you can use the standard form equation 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 semi-major axis length, and 'b' represents the semi-minor axis length.
In this case, the center is given as (-2, 3), the major axis length is 8 (which means the semi-major axis is 4), and the minor axis length is 2 (which means the semi-minor axis is 1). The major axis is parallel to the y-axis, indicating that 'a' will be in the y-direction and 'b' will be in the x-direction.
Plugging in these values, we get:
(x-(-2))^2/1^2 + (y-3)^2/4^2 = 1
Simplifying this equation gives:
(x+2)^2/1 + (y-3)^2/16 = 1
This is the equation of the ellipse satisfying the given conditions.