gaokao 2018 Q19

gaokao · China · national-II-science 12 marks Conic sections Circle-Conic Interaction with Tangency or Intersection

(12 points)
Let the focus of parabola $C : y ^ { 2 } = 4 x$ be $F$. A line $l$ passing through $F$ with slope $k ( k > 0 )$ intersects $C$ at points $A$ and $B$. $| A B | = 8$.
(1) Find the equation of line $l$;
(2) Find the equation of the circle passing through points $A$ and $B$ and tangent to the directrix of $C$.

(12 points)

Let the focus of parabola $C : y ^ { 2 } = 4 x$ be $F$. A line $l$ passing through $F$ with slope $k ( k > 0 )$ intersects $C$ at points $A$ and $B$. $| A B | = 8$.

(1) Find the equation of line $l$;

(2) Find the equation of the circle passing through points $A$ and $B$ and tangent to the directrix of $C$.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20