SAT1000 - P787

Geometry Level pending

As shown above, the focus of the parabola C:y2=2xC: y^2=2x is FF. Two lines l1,l2l_1, l_2 which are parallel to the x-axis intersect with CC at A,BA,B and intersect with the directix at P,QP,Q. MM is the midpoint of ABAB.

If SPQF=2SABFS_{\triangle PQF}=2S_{\triangle ABF}, find the locus of point MM.

If the locus can be expressed as f(x,y)=0f(x,y)=0, then when y=50y=50, submit the sum of all possible value(s) for xx.

Note: SABCS_{\triangle ABC} denotes the area of ABC\triangle ABC.

Have a look at my problem set: SAT 1000 problems


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