Question 1190882: Write the equation of the ELLIPSE that satisfies the given conditions
c. Center at (0, 0) one vertex (0, - 6) end of the minor axis (4,0)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to determine the equation of the ellipse:
**1. Identify the Center:**
The center is given as (0, 0).
**2. Determine the Orientation:**
Since a vertex is at (0, -6), which lies directly below the center, the major axis is vertical.
**3. Find 'a' (Semi-major Axis):**
The distance from the center (0, 0) to the vertex (0, -6) is 6 units. Therefore, a = 6.
**4. Find 'b' (Semi-minor Axis):**
The end of the minor axis is at (4, 0). The distance from the center (0, 0) to this point is 4 units. Therefore, b = 4.
**5. Write the Equation:**
The general equation of an ellipse centered at (h, k) with a vertical major axis is:
(x - h)² / b² + (y - k)² / a² = 1
Substitute the values we found (h = 0, k = 0, a = 6, b = 4):
(x - 0)² / 4² + (y - 0)² / 6² = 1
Simplify:
x² / 16 + y² / 36 = 1
Therefore, the equation of the ellipse is x²/16 + y²/36 = 1.
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