Question

Let \( a, b, c, d \) be non-zero numbers. If the point of intersection of the lines \( 4ax + 2ay + c = 0 \) and \( 5bx + 2by + d = 0 \) lies in the fourth quadrant and is equidistant from the two coordinate axes, then the relationship between \( a, b, c, d \) is:

• A. \( 3bc - 2ad = 0 \)
• B. \( 3bc + 2ad = 0 \)
• C. \( 2bc - 3ad = 0 \)
• D. \( 2bc + 3ad = 0 \)

Hint:

When a point lies in the fourth quadrant and is equidistant from the axes, use \( x = -y \) and solve the system of equations accordingly.

Answer 1

The Correct Option is A

Step 1: Solve the system of equations.
We substitute \( x = -y \) in both equations and simplify.
Step 2: Apply the equidistant property.
Using \( |x| = |y| \), we find the expressions for \( y \) in terms of \( a, b, c, d \).
Step 3: Solve for the relationship.
We get the relationship \( 3bc - 2ad = 0 \). Final Answer: \[ \boxed{3bc - 2ad = 0} \]