Question

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

Answer 1

Answer:
`\bold{x^2-(181)/(13)xy+12y^2=0}`

Explanation:

`\tan \theta =(y)/(x)\quad \longrightarrow \theta=\tan ^(-1)\bigg((y)/(x)\bigg)`

`\text{Given:}\quad \theta =\tan^(-1)\bigg((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=-(181)/(26)`

`\text{Insert:}\ h=-(181)/(26)`

`x^2 + 2\bigg(-(181)/(26)\bigg) xy + 12y^2 = 0`

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