Question

The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are

• A. \( 3x - 5y + 15 = 0, \quad 5x + 3y + 15 = 0 \)
• B. \( 5x - 3y + 15 = 0, \quad 3x + 5y + 15 = 0 \)
• C. \( 3x + 5y - 15 = 0, \quad 3y + 5x - 15 = 0 \)
• D. \( 3x + 5y + 15 = 0, \quad 5x + 3y + 15 = 0 \)

Hint:

For equations of lines with intercepts, use the general form \( \frac{x}{a} + \frac{y}{b} = 1 \) and solve for the intercepts.

Answer 1

The Correct Option is C

Step 1: General form of the equation.
The equation of a line with intercepts \( a \) and \( b \) is given by: \[ \frac{x}{a} + \frac{y}{b} = 1 \] From the problem, we know the sum of the intercepts is 8, and the product is 15. Thus, we have the system: \[ a + b = 8 \quad \text{and} \quad ab = 15 \]
Step 2: Solving the system.
Solving the system, we find the values of \( a \) and \( b \). Substituting into the equation of the line, we get the required equations: \[ 3x + 5y - 15 = 0, \quad 3y + 5x - 15 = 0 \]
Step 3: Conclusion.
Thus, the correct equations are \( 3x + 5y - 15 = 0 \) and \( 3y + 5x - 15 = 0 \), corresponding to option (C).