Ellipse Equation w/ only vertices and focus

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The ellipse has vertices at (2,3) and (-4,3) with a focus at (1,3), indicating a horizontal orientation. The center of the ellipse is calculated as (-1,3), and the distance from the center to the vertices gives a² = 9. The equation format is established as (x+1)²/b² + (y-3)²/9 = 1, but it requires an adjustment to include an equals sign on the right side. The relationship between a, b, and c for the ellipse needs to be used to determine the value of b. The final equation must be correctly formatted for clarity and accuracy.
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Homework Statement


Ellipse with vertex at (2,3) and (-4,3) and focus at (1,3)



Homework Equations


(x-h)2/a2 + (y-k)2/b2=1

The Attempt at a Solution


(h,k)= (-1,3)
a2=9
(x+1)2/ b2 + (y-3)2/ 92
 
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You have h and k correct. What is the equation relating a, b, and c for an ellipse? Use it to figure out b. And your final equation needs and = sign and a right hand side.
 

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