It is known that the left and right focal points of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 are F1 and F2 half focal length is c. the chord f1m of the ellipse is made through F1 and extended to N, so that Mn = MF2. It is proved that the trajectory of n is a circle and its equation is solved

Defined by ellipse
|MF1|+|MF2|=2a
From | Mn | = | MF2|
Then | Mn | + | MF1 | = 2A
|F1N|=2a
It is known that the distance from n to fixed point F1 (- C, 0) is fixed length 2A
equation
(x+c)^2+y^2=(2a)^2
(x+c)^2+y^2=4a^2

RELATED INFORMATIONS

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