Question

Please help me to solve the question. (chapter angle between two lines)​

Answer 1

Answer:    $\bold{x^2-\dfrac{181}{13}xy+12y^2=0}$

Step-by-step explanation:

$\tan \theta =\dfrac{y}{x}\quad \longrightarrow \theta=\tan ^{-1}\bigg(\dfrac{y}{x}\bigg)$

$\text{Given:}\quad \theta =\tan^{-1}\bigg(\dfrac{1}{13}\bigg)\quad \longrightarrow x=13,y=1$

Insert x = 13 and y = 1:

x² + 2hxy + 12y² = 0

(13)² + 2(13)(1) + 12(1)² = 0

169 + 26h + 12 = 0

       26h + 181 = 0

                26h = -181

                    $h=-\dfrac{181}{26}$

$\text{Insert:}\ h=-\dfrac{181}{26}$

$x^2 + 2\bigg(-\dfrac{181}{26}\bigg) xy + 12y^2 = 0$

$\bold{x^2 -\bigg(\dfrac{181}{13}\bigg) xy + 12y^2 = 0}$