# MT [238] inner track

Source: Internet
Author: User

It is known that \$ F_1 and F_2 \$ are the left and right focal points of the elliptical \$ C: \ dfrac {x ^ 2} {4} + \ dfrac {y ^ 2} {3} = 1 \$, point \$ p \$ when moving on an elliptical \$ C \$, \$ \ Delta {f_1pf_2} \$
Inner \$ I \$'s trajectory equation is _____

Analysis: Based on the internal vector, we can conclude that: \$ m \ overrightarrow {if_2} + n \ overrightarrow {if_1} + | f_1f_2 | \ overrightarrow {IP} = \ overrightarrow {o} \$
Note \$ P (x_0, y_0), I (x, y) \$ easy to know \$ m + n = 2a, M-N = 2x \$,
Bringing coordinates to the above formula \$ y_0 = 3Y, x_0 = 2x \$ to be substituted into \$ C: \ dfrac {x_0 ^ 2} {4} + \ dfrac {y_0 ^ 2} {3} = 1 \$ get \$ x ^ 2 + 3y ^ 2 = 1 (Y \ ne0) \$

MT [238] inner track

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