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Two tangent are drawn from the point `(-2,-1)`to parabola `y^2=4xdot`if `alpha`is the angle between these tangents, then find the value of `tanalphadot`A. 3B. 43468C. 2D. 43467 |
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Answer» Correct Answer - A The equation of a tangent to the parabola `y^(2)=4x` is `y=mx+1/m` If it passes through (-2, -1) then `-1=-2m+1/mrArr2m^(2)-m-1=0` Let `m_(1), m_(2)` be the roots of this equation. Then, `m_(1)+m_(2)=1//2" and "m_(1)m_(2)=-1//2` Now, `tanalpha+-(m_(1)-m_(2))/(1+m_(1)-m_(2))=+-(sqrt((m_(1)-m_(2))^(2)-4m_(1)-m_(2)))/(1+m_(1)-m_(2))` `rArr" "tanalpha=+-(sqrt(1//4+4//2))/(1-1//2)=+-(3//2)/(1//2)=+-3` |
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