The constant sum for the ellipse with the foci (-5,5) and (0,7) and the point (0,5) is 7
The foci of the ellipse are given as:
F1(−5, 5) aF2(0, 7)
The point is then given as:
Point (0, 5)
Calculate the distance between each focus and the point using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]F_1 = \sqrt{(-5-0)^2 + (5-5)^2}[/tex]
Evaluate
[tex]F_1 = 5[/tex]
Also, we have:
[tex]F_2 = \sqrt{(0-0)^2 + (7-5)^2}[/tex]
Evaluate
[tex]F_2 = 2\\[/tex]
The constant sum is then calculated using:
Constant sum = F1 + F2
So, we have:
Constant sum = 5 + 2
Evaluate
Constant sum = 7
Hence, the constant sum is 7
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