To write: the equation of the ellipse.
Given information:
The vertices of the ellipse are at
Formula Used:
Standard equation of an Ellipse
Equation | Major Axis | Vertices | Co-vertices |
Horizontal | |||
Vertical |
The center of the Ellipse is
Eccentricity of conic sections
The eccentricity of each conic section is defined below. For an ellipse or hyperbola, c is the distance from each focus to the center, and a is the distance from each vertex to center.
Circle:
Parabola:
Ellipse:
Hyperbola:
Explanation:
Center of the ellipse is at the middle of the two vertices.
Since, the y co-ordinates are same, so it has horizontal major axis and has the form:
The center is between -6 and 6.
So, the center is at
Distance from center to vertex a :
It is given that the eccentricity of the given ellipse is:
Now, find the distance from the center to co-vertex b .
Now susbtitute these values in the standard equation of ellipse.
Chapter 8 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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