SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±5, 0); major axis of length 14

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Question 1176239: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Foci: (±5, 0); major axis of length 14
Answer by MathLover1(20850) About Me  (Show Source):
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Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1
center is at (0,0)
Foci: (5,+0), (-5, 0)
focus is 5 units from the center, so c+=+5 and
major axis of length 2a=14->a=7
use the equation b%5E2+%2B+c%5E2+=+a%5E2 to find b%5E2
b%5E2++=+a%5E2-c%5E2
b%5E2++=+7%5E2-5%5E2
b%5E2++=+49-25
b%5E2++=+24
your equation is:
x%5E2%2F49%2By%5E2%2F24=1