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Question 471709: Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 18, and foci at (0,-12) and (0,12).
a. (x^2/225)+(y^2/81)=1
b. (x^2/144)+(y^2/81)=1
c. (x^2/81)+(y^2/225)=1
d. (x^2/9)+(y^2/15)=1
e. (x^2/15)+(y^2/9)=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 18, and foci at (0,-12) and (0,12).
a. (x^2/225)+(y^2/81)=1
b. (x^2/144)+(y^2/81)=1
c. (x^2/81)+(y^2/225)=1
d. (x^2/9)+(y^2/15)=1
e. (x^2/15)+(y^2/9)=1
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Based on given data, this is an equation of an ellipse with vertical major axis of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the center.
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Normally, a complete solution would be required, but because this is a multiple choice question, we can save some steps in determining the correct answer. (Assuming one of the choices is a correct answer)
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First, since the center is at (0,0), h and k will not appear in the equation.
Since this ellipse has a vertical major axis, a^2, the larger number will appear under the y-term.
Given length of minor axis=18=2b
b=9
b^2=81 (this is the smaller number that should be under the x-term)
From this information we can conclude that c. (x^2/81)+(y^2/225)=1 is the right answer.
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Calculating a^2 is not necessary for selecting the right multiple choice, but if required, this is how you can do it:
Foci:
c=distance from center to one focal point=12
c^2=144
c^2=a^2-b^2
a^2=c^2+b^2=144+81=225
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