The equation of an ellipse for the graph shown is [tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
How to determine the equation?
Since the given coordinates of the vertices and foci have the form (-5, 0) and (5, 0) and (-2, 0) and (2, 0) respectively, this ultimately implies that the major axis of this ellipse is the x-axis.
Thus, the standard form of the equation of this ellipse is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Next, we would solve for b² by using this equation:
b² = a² - c²
b² = 5² - 2²
b² = 25 - 4
b² = 21.
Substituting the parameters into the standard equation of an ellipse, we have;
[tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
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