Question

product of the intercepts of a straight line is 1 passes through (-12, 1) then its equation is

Answer 1

Given:

1. Product of the intercepts of a straight line = 1
2. The line passes through (-12, 1)

To find:

1. Equation of line

Answer:

• Let us consider the equation of line given by -
• $\frac{x}{a} +\frac{y}{b} =1$   -(1)
• Here, a is the intercept on X-axis and b is the intercept on Y-axis.
• It is given that the product of the intercepts of the line is 1
• Hence, a*b = 1.
• a = 1/b   -(2)
• We also know that the line passes through (-12, 1).
• Substituting the point and equation 2 in equation 1 -
• $\frac{-12}{1/b} + \frac{1}{b} = 1$

• 1 + 12b = 1/b
• b + 12b² - 1= 0
• b1 = 1/4 and b2 = -1/3
• From equation 1 we get a1 = 4 and a2 = -3 respectively.
• Thus the equation of line from (a1, b1) is  $\frac{x}{4} + 4y = 1$
• This is expressed as x + 16y = 4.

• Thus the equation of line from (a2, b2) is $\frac{x}{-3} + \frac{3y}{-1} = 1$
• This is expressed as x + 9y = -3.

Thus, there are two lines whose product of the intercepts is 1 and pass through (-12, 1). Their equations are x + 16y = 4 and x + 9y = -3.