Show the following equation represents pair of the lines.find, also the angle between them 6x2+13xy +6y2+8x+7y+2=0
Answers
Hence it is shown that the 6x2+13xy +6y2+8x+7y+2=0 equation represents pair of the lines. Also angle between them is ∅ = tan^{-1} 5/12
The angle between pair of straight lines represented by a standard equation given by,
ax^2 + 2hxy + by^2 + 2gx + 2fy +c = 0 ..........(1)
Given equation,
6x^2 + 13xy + 6y^2 + 8x + 7y + 2 = 0 ...........(2)
Comparing (1) and (2) it's clear that, the given equation represents the pair of lines.
In order to find the angle between the lines, we use formula,
tan ∅ = | (2 √( h^2 – ab) ) / (a+b) | .............(3)
comparing the equations (1) and (2), we get,
a = 6, b = 6, h = 13/2, g = 4, f = 7/2, c= 2
substituting the above values in equation (3), we get,
tan ∅ = | (2 √( (13/2) ^2 – 6 . 6 ) ) / (6 + 6) |
tan ∅ = | (2 √( 6.25 ) ) / 12 |
tan ∅ = | 5/12 |
Hence ∅ = tan^{-1} 5/12