TS EAMCET · Maths · Straight Lines

The slope of a line $L$ is $2 .$ If $m_{1}, m_{2}$ are slopes of two lines which are inclined at an angle of $\frac{π}{6}$ with $L,$ then $m_{1} + m_{2} =$

A $- 11$
B $16$
C $11$
D $- 16$

Verified Solution

Answer & Solution

Correct Answer

(D) $- 16$

Step-by-step Solution

Detailed explanation

Angle between two lines, tanθ=m-m'1+mm' ⇒tanπ6=m-21+2m2 Squaring both the sides ⇒4m2+4m+113=m2-4m+4 ⇒4m2+4m+1=3m2-12m+12 ⇒m2+16m-11=0, where roots are m1 & m2 So, =m1+m2=-161=-16

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The slope of a line L is 2. If m1, m2 are slopes of two lines which are inclined at an angle of π6 with L, then m1+m2=

Step-by-step Solution

The slope of a line $L$ is $2 .$ If $m_{1}, m_{2}$ are slopes of two lines which are inclined at an angle of $\frac{π}{6}$ with $L,$ then $m_{1} + m_{2} =$