Question 1087976: Find the standard form of the equation of the ellipse with foci at (0,0) and (4,0), and has a major axis of length 6. Answer by ikleyn(52803) (Show Source):
From the condition:
The major axis (connecting foci) is the horizontal line y = 0, coinciding with x-axis.
The center of the ellipse is the midpoint between the foci, i.e. (2,0).
The focal distance is 2c = 4 - 0 = 4; Hence, the distance from the center to each focus is c = = 2.
Since the major axis length is 6, the major seni-axis is = 3.
Then the minor semi-axis is = = = 5.
Thus the standard form of the ellipse equation is
+ = 1.
The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".
