1)

Let PQ be a focal chord of the parabola y2=4ax.The tangents to the parabola at P and Q meet at point lying on the line y=2x+a, a >0

 Length  of chord PQ is 


A) 7a

B) 5a

C) 2a

D) 3a

Answer:

Option B

Explanation:

Concept involved

 Intersection point of tangents at  (at21,2at1) and (at22,2at2) is ( at1t2 , a/t1 +t2) ) , also tangents drawn  at end point of focal chord are perpendicular and intersect on directrix

 Since  R(a,a(t1t))  lies on y =2x+a

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    a.(t1t)=2a+a

      t1t=1

 Thus, length of focal chord

 a(t+1t)2=a{(t1t)2+4}=5a