Standard form of an eqation

Question

Write the standard form equation of the ellipse with vertices (-5, 4) and (8, 4) and whose focus is (-4, 4).

Answer 1

Find the center of the ellipse:

Center = midpoint of the vertices

          =((-5+8)/2,(4+4)/2)

          =(3/2,4)

Distance between the vertices:

2a = √((8-(-5))²+(4-4)²)

      =13

a =13/2

Distance from center to focus:

c =√((-4-(3/2))²+(4-4)²)

   =√((-11/2)²

  =√(121/4)

  =11/2

b²=a² - c²

    =(13/2)² - (11/2)²

    =48/4

    =12

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Standard equation

(x-3/2)²/(13/2)²+(y-4)²/12