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Write the equation of an ellipse with the following characteristics: center =(1,-3) vertices=(-6,-3),(8,-3)
Foci =(-4.7,-3),(6.7,-3)

Sagot :

Answer:

(x-1)²/49 + (y+3)²/16.51 = 1

Step-by-step explanation:

vertex (8,-3)     Foci (6.7,-3)   center (h,k) = (1,-3) , major axis parallel to x axis

a  is the distance of the vertex from the center, and c   is the distance of the foci from the center. b is semi-minor axis

b² = a² - c²         Ellipse equation: (x-h)²/a² + (y-k)²/b² = 1

a = 8-1 = 7         c = 6.7 - 1 = 5.7

b² = 7² - 5.7² = 16.51

Ellipse equation:  (x-1)²/49 + (y- -3)²/16.51 = 1  i.e. (x-1)²/49 + (y+3)²/16.51 = 1

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