The equation that represent the eclipse in the image attached is option A.
What is the ellipse equation about?
We were given:
The center of an ellipse (0, 0).
One focus is located at (12, 0),
One directrix is at x = 14 1/12.
To Find the equation of the ellipse will be:
The standard equation of an ellipse is : [tex]\frac{(x- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]
Note that c = 12
One need to compare the equation of directrix with the above equation:
a^2/c = 14[tex]\frac{1}{12}[/tex]
a^2/c = 169/12
Then Substitute the value c=12 and solve for a.
a^2/12 = 169/12
a² = 169
a = 13
Use the equation of c² = a² - b² to find b.
= (12)² = (13/12)² - b²
b²= 169-144
b²= 25
b = 5
Then substitute the value of a and b into the standard equation of the ellipse.
[tex]\frac{(a- h )^ 2}{a^2} + \frac{(y - k)^2}{b^2}[/tex]
[tex]\frac{(x- 0 )^ 2}{13^2} + \frac{(y - 0)^2}{5^2}[/tex]
Therefore: [tex]\frac{(x)^ 2}{13^2} + \frac{(y)^2}{5^2}[/tex]
Hence, The equation that represent the eclipse in the image attached is option A.
Learn more about eclipse from
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