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  • A line is passing through (1,1) and and another line which is passing through

A line is passing through (1,1) and (2,1+\sqrt{3}) and another line which is passing through (1,1) and (2,1+\frac{1}{\sqrt{3}}) then find the equation of line which is equally inclined with both line .

Option: 1

y=x


Option: 2

y=-x


Option: 3

Option A and B both


Option: 4

None of these


Answers (1)

best_answer

 

 

Line Equally Inclined with two lines -

Line Equally Inclined with two lines

If the two lines with slope m1 and m2 are equally inclined to a line having slope m, then 

Two lines with slope m1 and m2 intersect at point A

 

As from the fig

Hence,

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\text{Slope of line }L_1=\frac{1+\sqrt{3}-1}{2-1}=\sqrt{3}=\tan 60^{\circ}\\ \text{Slope of line }L_2=\frac{1+\frac{1}{\sqrt{3}}-1}{2-1}=\frac{1}{\sqrt{3}}=\tan 30^{\circ}\\ \text{Slope of line which is equally inclined }=\tan 45^{\circ}=1\\ \text{and another line which is also equally inclined,slope is }=-1\\ \text{Equations of lines}\\ L_1: \ y-1=x-1\\\Rightarrow y-x=0\\ L_2: \ y-1=-1(x-1)\\\Rightarrow y+x-2=0\\

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Ajit Kumar Dubey

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