The equation of the pair of bisectors of the angles between two straight lines is, 12x^2 - 7xy - 12y^2 = 0. if the equation of one line is 2y - x = 0 then the equation of other line is?
Answers
Then the pair of bisectors of the angles between them is :
h (x² - y²) = (a - b) x y
we are given: pair of bisectors: 12 (x² - y²) = 7 xy
so h = 12 and (a-b) = 7
So pair of intersecting lines: (7+b) x² + 24 xy + b y² = 0
one of the lines is 2 y - x = 0
so (2 y - x) * [ b/2 y - (7+b) x ] = (7+b) x² + 24 xy + b y²
equating coefficients: - b/2 - 2(7+b) = 24
=> b = -76/5
so a = b+7= -41/5
so the other line : b/2 y - (7+b) x = 0
-38/5 y +41/5 x = 0
38 y - 41 x = 0
pair of intersecting lines : 41 x² - 120 xy + 76 y² = 0
Answer:
Step-by-step explanation:
Let the pair of intersecting lines be represented by: ax² +2hxy + by² = 0
Then the pair of bisectors of the angles between them is :
h (x² - y²) = (a - b) x y
we are given: pair of bisectors: 12 (x² - y²) = 7 xy
so h = 12 and (a-b) = 7
So pair of intersecting lines: (7+b) x² + 24 xy + b y² = 0
one of the lines is 2 y - x = 0
so (2 y - x) * [ b/2 y - (7+b) x ] = (7+b) x² + 24 xy + b y²
equating coefficients: - b/2 - 2(7+b) = 24
=> b = -76/5
so a = b+7= -41/5
so the other line : b/2 y - (7+b) x = 0
-38/5 y +41/5 x = 0
38 y - 41 x = 0
pair of intersecting lines : 41 x² - 120 xy + 76 y² = 0