Answer:
The distance between the center and the foci is √13 ≅ 3.6 units
Step-by-step explanation:
* Lets revise the equation of the ellipse
- The standard form of the equation of an ellipse with center
(0 , 0) and major axis parallel to the x-axis is
x²/a² + y²/b² = 1
# a > b
- The length of the major axis is 2a
- The coordinates of the vertices are (± a , 0)
- The length of the minor axis is 2b
- The coordinates of the co-vertices are (0 , ± b)
- The coordinates of the foci are (± c , 0), where c² = a² − b²
* Lets solve the problem
∵ The equation is x²/49 + y²/36 = 1
∴ a² = 49
∴ b² = 36
∵ The coordinates of the foci are (± c , 0)
∵ c² = a² − b²
∴ c² = 49 - 36 = 13 ⇒ take square root for both sides
∴ c = ± √13
∴ The foci are (√13 , 0) and (-√13 , 0)
∵ The center is (0 , 0)
∴ The distance between the center and the foci is c - 0 = c or
0 - (-c) = c
∴ The distance between the center and the foci = √13 - 0 = √13 units
* The distance between the center and the foci is √13 ≅ 3.6 units
