If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12 , then the length of its latus rectum is:
If y=mx+4 is a tangent to both the parabolas, and
then b is equal to :
Let $A(1,0), B(6,2)$ and $C\left(\frac{3}{2}, 6\right)$ be the vertices of a triangle ABC . If P is a point inside the triangle $A B C$ such that the triangles $A P C, A P B$ and $B P C$ have equal areas, then the length of the line segment PQ , where Q is the point $\left(-\frac{7}{6},-\frac{1}{3}\right)$, is