Question 472587: 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).
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Based on given data, equation is that 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 (x,y) coordinates of the center./
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Center: (0,0)
Length of minor axis=18=2b
b=9
b^2=81
..
c=12
c^2=144
..
c^2=a^2-b^2
a^2=c^2+b^2=144+81=225
..
Equation: (x-0)^2/81+(y-0)^2/225=1
Ans: c. (x^2/81)+(y^2/225)=1
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