AP EAMCET · Maths · Pair of Lines

The acute angle between lines $6 x^{2} + 11 x y - 10 y^{2} = 0$ is

A $\tan^{- 1} (\frac{\sqrt{361}}{2})$
B $\tan^{- 1} (\frac{\sqrt{361}}{4})$
C $\tan^{- 1} (\frac{361}{2})$
D $\tan^{- 1} (\frac{361}{4})$

Verified Solution

Answer & Solution

Correct Answer

(B) $\tan^{- 1} (\frac{\sqrt{361}}{4})$

Step-by-step Solution

Detailed explanation

Acute angle between pair of straight lines ax2+2hxy+by2=0 is given by tanθ=2h2-aba+b By comparing the given equation of lines with ax2+2hxy+by2=0 we get a=6,b=-10,h=112 Then, tanθ=21214+60-4=361-4 ⇒θ=tan-13614

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 acute angle between lines 6x2+11xy-10y2=0 is

Step-by-step Solution

The acute angle between lines $6 x^{2} + 11 x y - 10 y^{2} = 0$ is