a straight line x by a minus y by b equals to 1 passes through the point 86 and Cuts of a triangle of area 12 units from the axis of coordinates
Answers
Equations of line are 3x - 2y = 12 or 3x - 8y + 24 = 0
Step-by-step explanation:
Hi,
Given a straight line x/a - y/b = 1----------(1)
Given line passes through the point (8, 6) , hence
8/a - 6/b = 1
8/a = (1 + 6/b) = (b + 6)/b
a = 8b/(b + 6)-----(2)
Points of intersection of the given line with the coordinate axes are
A(a, 0) and B( 0, -b)
Hence the area of the triangle formed by the coordinate axes is
1/2|ab| = 12
|ab| = 24
ab = 24 or -24
Case 1: Suppose ab = 24
From equation (2),
a = 8b/(b + 6),
8b²/b+6 = 24
⇒ b² = 3b + 18
⇒ b² - 3b - 18 = 0
⇒ (b² - 6b + 3b - 18) = 0
b = 6 or b = -3
If b = 6 , a = 4 ,
Equation of line is x/4 - y/6 = 1 or 3x - 2y = 12
If b = -3 , a = -8,
Equation of line is x/-8 - y/-3 = 1 or 3x - 8y + 24 = 0
Case 2: Suppose ab = -24
From equation (2),
a = 8b/(b + 6),
8b²/b+6 = -24
⇒ -b² = 3b + 18
⇒ b² + 3b + 18 = 0
b does not have real roots
Equations of line are 3x - 2y = 12 or 3x - 8y + 24 = 0
Hope, it helps !