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Let PQ be a focal chord of the parabola `y^2 = 4ax` The tangents to the parabola at P and Q meet at a point lying on the line `y = 2x + a, a > 0`. Length of chord PQ isA. 7aB. 5aC. 2aD. 3a |
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Answer» Correct Answer - B Let `(at_(1)^(2),2at_(1))" and "Q(at_(2)^(2),at_(2))` be the end-point of a focal chord of the parabola `y^(2)=4ax`. Then, `t_(1)t_(2)=-1" and "PQ=a(t_(2)-t_(1))^(2)`. The tangents at P and Q intersect at a point `(at_(1)t_(2),a(t_(1)+t_(2)))` which lies on y = 2x + a. `:." "e(t_(1)+t_(2))=2at_(1)t_(2)+a` `rArr" "t_(1)+t_(2)=-2+1+1` `rArr" "t_(1)+t_(2)=-2+1=-1" "[becauset_(1)t_(2)=-1]` `:." "PQ=a(t_(2)-t_(1))^(2)` `=a{(t_(2)+ty_(1))^(2)-4t_(1)t_(2)}=a[(-1)^(2)-4(-1)]=5a` |
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