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AB, AC are tangents to a parabola `y^(2)=4ax`. If `l_(1),l_(2),l_(3)` are the lengths of perpendiculars from A, B, C on any tangent to the parabola, thenA. `l_(1), l_(2), l_(3)` are in GPB. `l_(2), l_(1), l_(3)` are in GPC. `l_(3), l_(1), l_(2)` are in GPD. `l_(3), l_(2), l_(1)` are in GP |
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Answer» Correct Answer - B::C Let the coordinates of B C be `(at_(1)^(2), 2at_(1))` and `(at_(1)t_(2), a(t_(1)+t_(2))` respectively. Then, the coordinates of A are `(at_(1)t_(2), a(t_(1)+t_(2))` The equation of any tangent to `y^(2)=4ax` is `ty=x+aty^(2)` `:." "l_(1)=(at_(1)t_(2)-a(t_(1)-t_(2))t+at^(2))/(sqrt(1+t^(2)))` Clearly, `l_(2)l_(3)=l_(1)^(2)`. Therefore, `l_(2)l_(1)l_(3)` are om G.P. |
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