Question 168
In a plane rectangular coordinate system $xOy$ there are three points $A(0, \frac{4}{3})$, $B(-1, 0)$ and $C(1, 0)$. The distance from point $P$ to line $BC$ is the geometric mean of the distances from this point to lines $AB$ and $AC$.
(1) Find the locus equation of point $P$.
(2) If line $L$ passes through the incenter (say, $D$) of $\triangle ABC$, and has exactly 3 common points with the locus of point $P$. Determine all values of the slope $k$ of line $L$.
(1) Find the locus equation of point $P$.
(2) If line $L$ passes through the incenter (say, $D$) of $\triangle ABC$, and has exactly 3 common points with the locus of point $P$. Determine all values of the slope $k$ of line $L$.