Question 1190883: Write the equation of the ELLIPSE that satisfies the given conditions
d. Vertices (-5,0) and (5,0) length of latus rectum 8/5
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to find the equation of the ellipse:
**1. Center and Orientation:**
The vertices are at (-5,0) and (5,0). This tells us:
* The center of the ellipse is at the origin (0,0).
* The major axis is horizontal (along the x-axis).
**2. Value of 'a':**
The distance from the center to a vertex is 'a'. Since the vertices are at (-5,0) and (5,0), we have a = 5.
**3. Latus Rectum:**
The length of the latus rectum is given as 8/5. The formula for the latus rectum is (2b²)/a.
**4. Solve for 'b²':**
We can use the latus rectum length and the value of 'a' to solve for b²:
8/5 = (2b²) / 5
8 = 2b²
b² = 4
**5. Equation of the Ellipse:**
Since the major axis is horizontal, the standard form of the equation is:
(x²/a²) + (y²/b²) = 1
Substitute the values of a² and b²:
(x²/5²) + (y²/4) = 1
(x²/25) + (y²/4) = 1
Therefore, the equation of the ellipse is (x²/25) + (y²/4) = 1.
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