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If the two focal points of the ellipse x ^ 2 / 25 + y ^ 2 / 9 = 1 are F1 and F2 respectively, and point P is any point on the ellipse, find the perimeter of pf1f2?
It is known that a = 5, B = 3, so C = 4, then F1F2 = 2C = 8,
According to the definition of ellipse, Pf1 + PF2 = 2A = 10, so the perimeter of pf1f2 is 18
Let F1 and F2 be the focus of the ellipse C: X225 & nbsp; + Y29 = 1, and P & nbsp; be a point on the ellipse, then the perimeter of △ pf1f2 is______ ．
From the ellipse C: X225 & nbsp; + Y29 = 1, A2 = 25, B2 = 9, a = 5, B = 3, C = A2 − B2 = 4. Then the perimeter of △ pf1f2 = | Pf1 | + | PF2 | + | F1F2 | = 2A + 2C = 2 × 5 + 2 × 4 = 18
Ellipse focus F1 (- 3,0) F2 (3,0), P is the point on the ellipse, and | F1F2 | is the mean difference between | Pf1 | and | PF2 | to solve the elliptic equation
From the meaning of the title
c=3 |F1F2|=6
|F1F2 | is the median of | Pf1 | and | PF2 |
So | Pf1 | + | PF2 | = 2A = 12
a=6 b²=27
The elliptic equation is X & sup2 / 36 + Y & sup2 / 27 = 1
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