SAT1000 - P802

Geometry Level pending

As shown above, the parabola C1:x2=yC_1: x^2=y, circle C2:x2+(y4)2=1C_2: x^2+{(y-4)}^2=1, and MM is the center of circle C2C_2.

Point PP is a point on C1C_1 (not at (0,0)(0,0)), and l1,l2l_1, l_2 are two lines tangent to C2C_2 and they intersects with C1C_1 at point A,BA,B respectively. Line ll passes through MM and PP.

If lABl \perp AB, find the equation of line ll.

The equation can be expressed as: y=±kx+b (k>0)y=\pm k x+b\ (k>0) . Submit 1000(k+b)\lfloor 1000(k+b) \rfloor.

Have a look at my problem set: SAT 1000 problems


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