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Two mutually perpendicular tangents of the parabola `y^(2)=4ax` meet the axis at `P_(1)andP_(2)`. If S is the focal of the parabola, Then `(1)/(SP_(1))+(1)/(SP_(2))` is equal toA. `(1)/(2a)`B. `(1)/(a)`C. `(2)/(a)`D. `(4)/(a)` |
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Answer» Correct Answer - B (2) Tangents at `A(t_(1))andA(t_(2))` are respectively, `t_(1)y=x+at_(1)^(2)` `t_(2)y=x+at_(2)^(2)` Tangent meet axis at `P_(1)(-at_(1)^(2),0)andP_(2)(-at_(2)^(2),0)`. `:." "SP_(1)=a+at_(1)^(2),andSP_(2)=a+at_(2)^(2)` Since tangents are perpendicular, `t_(1)t_(2)=-1`. `:.(1)/(SP_(1))+(1)/(SP_(2))=(1)/(a+at_(1)^(2))+(1)/(a+at_(2)^(2))` `=(1)/(a+at_(1)^(2))+(1)/a+(a)/(t_(1)^(2))` `=(1)/(a+at_(1)^(2))+(t_(1)^(2))/(at_(1)^(2)+a)` `(1)/(a)` y-x-0 |
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