SOLUTION: Find an equation in standard form for the ellipse with center at (5, 8), horizontal axis of length 10 and passes through the point (6, 4).

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Question 1204201: Find an equation in standard form for the ellipse with center at (5, 8), horizontal axis of length 10 and passes through the point (6, 4).
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We can't tell with the given information whether the horizontal axis is the major or minor axis. We can assume it is the major axis and then adjust our results if it turns out that it is the minor axis.

The standard form with center at (5,8) and horizontal major axis of length 10 is

%28x-5%29%5E2%2F5%5E2%2B%28y-8%29%5E2%2Fb%5E2=1

Find b^2 using the given point (6,4) on the ellipse.

%286-5%29%5E2%2F5%5E2%2B%284-8%29%5E2%2Fb%5E2=1
1%2F25%2B16%2Fb%5E2=1
16%2Fb%5E2=24%2F25
24b%5E2=400
b%5E2=400%2F24=50%2F3

Note that b^2=50/3 is less than a^2=25, so the horizontal axis is indeed the major axis.

The standard form of the equation of the ellipse is

ANSWER: %28x-5%29%5E2%2F25%2B%28y-8%29%5E2%2F%2850%2F3%29=1

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation in standard form for the ellipse with center at (5, 8),
horizontal axis of length 10 and passes through the point (6, 4).
%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1



Substitute a=10/2=5.  h=5, k=8, x=6, y=4

%286-5%29%5E2%2F5%5E2%2B%284-8%29%5E2%2Fb%5E2=1

%281%29%5E2%2F25%5E%22%22%2B%28-4%29%5E2%2Fb%5E2=1

1%5E%22%22%2F25%5E%22%22%2B16%5E%22%22%2Fb%5E2=1

Multiply through by 25b2.

b%5E2%2B400=25b%5E2
400=24b%5E2
400%2F24=b%5E2
50%2F3=b%5E2
sqrt%2850%2F3%29=b

%28x-5%29%5E2%2F5%5E2%2B%28y-8%29%5E2%2F%2850%2F3%29=1

Edwin