A straight line x/a -y/b =1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of coordinates .find the equation of straight line

3 answers

since (8,6) lies on it,
8/a - 6/b = 1
(8b - 6a)/(ab) = 1
8b - 6a = ab
8b - ab = 6a
b(8 - a) = 6a
b = 6a/(8-a) **

x/a - y/b = 1 is in the intercept form, that is
the x-intercept is (a,0)
the y-intercept is (0,b)
so the area of the triangle is (1/2)(ab)
(1/2)(ab) = 12
ab = 24 ***

sub ** into ***
a(6a)/(8-a) = 24
6a^2 = 192 - 24a
a^2 + 4a - 32 = 0
(a+8)(a-4) = 0
a = -8 or a = 4

if a = 4, b = 6
x/4 - y/6 = 1 ---> 6x - 4y = 24 or 3x - 2y = 12

if a = -8, b = -3
x/-8 - y/-3 = 1 ---> -3x + 8y = 24 or 3x - 8y = -24

Very useful