gaokao 2018 Q20

gaokao · China · national-II-arts 12 marks Conic sections Circle-Conic Interaction with Tangency or Intersection
Let the parabola $C : y ^ { 2 } = 4 x$ have focus $F$. A line $l$ through $F$ with slope $k ( k > 0 )$ intersects $C$ at points $A , B$, with $| A B | = 8$.
(1) Find the equation of $l$;
(2) Find the equation of the circle passing through points $A , B$ and tangent to the directrix of $C$.
Let the parabola $C : y ^ { 2 } = 4 x$ have focus $F$. A line $l$ through $F$ with slope $k ( k > 0 )$ intersects $C$ at points $A , B$, with $| A B | = 8$.\\
(1) Find the equation of $l$;\\
(2) Find the equation of the circle passing through points $A , B$ and tangent to the directrix of $C$.