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  • The angle between the lines represented by <img alt="\mathrm{x^{2}-7 x y+12 y^{2}=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E%7B2%7D-7%20x%20y&plus;12%20y%5E%7B2%7

The angle between the lines represented by \mathrm{x^{2}-7 x y+12 y^{2}=0} is:

Option: 1

45^{\circ}


Option: 2

60^{\circ}


Option: 3

15^{\circ}


Option: 4

None of these


Answers (1)

best_answer

 We know that if the angle between the lines \mathrm{a x^{2}+2 h x y+b y^{2}=0}  is \mathrm{\theta} then

\mathrm{\tan \mathrm{q}=\frac{2 \sqrt{\mathrm{h}^{2}-\mathrm{ab}}}{(\mathrm{a}+\mathrm{b})}}
Here \mathrm{a=1, b=12\, and \, h=-\frac{7}{2}}
\text { So } \tan q=\frac{2 \sqrt{\frac{49}{4}-12}}{1+12}=\frac{1}{13} \\
q=\tan ^{-1} \frac{1}{13}
Hence (D) is the correct answer.

Posted by

Devendra Khairwa

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