Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and , respectively.
The equations of the lines are and .
Explanation
This question tests the understanding of the intercept form of a line. From the textbook context, the intercept form is given as x/a + y/b = 1, where a is the x-intercept and b is the y-intercept. Students need to find the values of a and b using the given conditions (sum = 1, product = -6), then substitute these values into the intercept form equation.
Solution Steps
Step 1: Let a be the x-intercept and b be the y-intercept. According to the question, we have: Sum of intercepts: a + b = 1, Product of intercepts: ab = -6
Step 2: From a + b = 1, we get b = 1 - a. Substituting in ab = -6: a(1 - a) = -6, which gives a - a² = -6, or a² - a - 6 = 0
Step 3: Solving the quadratic equation a² - a - 6 = 0: (a - 3)(a + 2) = 0. Therefore, a = 3 or a = -2
Step 4: When a = 3: b = 1 - 3 = -2. When a = -2: b = 1 - (-2) = 3
Step 5: Using the intercept form x/a + y/b = 1 from the textbook: For a = 3, b = -2: x/3 + y/(-2) = 1, which simplifies to 2x - 3y = 6
Step 6: For a = -2, b = 3: x/(-2) + y/3 = 1, which simplifies to -3x + 2y = 6 or 3x - 2y + 6 = 0