SAT1000 - P767

Geometry Level pending

As shown above, the hyperbola: x2a2y2b2=1 (a>0,b>0)\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1\ (a>0,b>0) has right focus point FF, right vertex AA.

Line l1l_1 passes through FF and it intersects with the hyperbola at point B,CB,C, l2l_2 passes through BB and l2ACl_2 \perp AC, l3l_3 passes through CC and l2ABl_2 \perp AB, l2,l3l_2, l_3 intersects at point DD.

If the distance from DD to line l1l_1 is less than a+a2+b2a+\sqrt{a^2+b^2}, what is the range of the slope of the hyperbola's asymptotes?

Have a look at my problem set: SAT 1000 problems


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