Question

Find what straight line is represented by the equation x^2 - 7xy + 12y^2 = 0

Answer 1

Brainly.in

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Secondary SchoolMath 8 points

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?

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kvnmurty

kvnmurty

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