2%2F25-%2B-(y-%2B-1)2%2F16-%3D-1.jpeg "(x – 3)2/25 + (y + 1)2/16 = 1")
Ellipse Equation: (x – 3)²/25 + (y + 1)²/16 = 1
In this article, we will discuss the ellipse equation (x – 3)²/25 + (y + 1)²/16 = 1. We will explore the graph of the equation, its center, vertices, and foci.
Graph of the Equation
The equation (x – 3)²/25 + (y + 1)²/16 = 1 represents an ellipse centered at (3, -1). The graph of the equation is as follows:
<h2 align="center"> <img src="https://latex.artofproblemsolving.com/8/3/1/831c5fa5c4b37fba91a71cfe61d2c1e5a4b42f96.png" alt="Graph of the equation" /> </h2>
Center of the Ellipse
The center of the ellipse is (3, -1). This is evident from the equation, where the center is shifted 3 units to the right and 1 unit down from the origin.
Vertices of the Ellipse
The vertices of the ellipse are the points where the ellipse intersects the axes. In this case, the vertices are (8, -1) and (-2, -1).
Foci of the Ellipse
The foci of the ellipse are the points (5.48, -1) and (0.52, -1). These points are calculated using the formula c = sqrt(a² - b²), where a is the semi-major axis and b is the semi-minor axis.
Properties of the Ellipse
- The semi-major axis is 5 units (
a = 5). - The semi-minor axis is 4 units (
b = 4). - The eccentricity of the ellipse is
e = 0.6.
In conclusion, the equation (x – 3)²/25 + (y + 1)²/16 = 1 represents an ellipse centered at (3, -1) with vertices (8, -1) and (-2, -1), and foci (5.48, -1) and (0.52, -1).
