SOLUTION: "How do I write the equation for ellipse with center (3,5) , vertex (-10,5), and focus (8,5) "

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Question 951643: "How do I write the equation for ellipse with center (3,5) , vertex (-10,5), and focus (8,5) "
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
For an ellipse with major axis horizontal:
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1
Where (h,k) is the center,
a is distance from center to vertex,
b is distance from center to co-vertex,
The co-vertex is the intersection of the ellipse and the minor axis.
b can also be calculated from the equation b%5E2=a%5E2-c%5E2 where a is distance from center to vertex, c is distance from center to focus.
In this case:
a=13 (from (3,5) to (-10, 5) the distance from 3 to -10=13
c=5 (from (3,5) to (8,5) the distance from 3 to 8=5
b=sqrt(a^2-c^2)}}}=sqrt%2813%5E2-5%5E2%29=sqrt%28144%29=12
The equation becomes:
%28x-3%29%5E2%2F169%2B%28y-5%29%5E2%2F144=1