If P is a point on a fixed ellipse (the length of major axis, the length of minor axis and the length of focal length are 2a, 2b and 2C respectively, and the focus is F1 and F2), If the maximum value of | Pf1 | PF2 | is 16 and the minimum value is 7, then what are a and B equal to? Why? | Math enthusiast | Mathematical art

If P is a point on a fixed ellipse (the length of major axis, the length of minor axis and the length of focal length are 2a, 2b and 2C respectively, and the focus is F1 and F2), If the maximum value of | Pf1 | PF2 | is 16 and the minimum value is 7, then what are a and B equal to? Why?

|The minimum value of Pf1 | PF2 | is 7
That is, P is at the end of the long axis
|PF1||PF2|=(a+c)(a-c)=a^2-c^2=b^2=7
b=√7
|The maximum value of Pf1 | PF2 | is 16
That is, P is at the end of the minor axis
|PF1||PF2|=c^2+b^2=a^2=16
a=4

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