A line passing through origin and is perpendicular to two given lines and . The ratio in which the origin divides points of intersection of given lines and the line perpendicular to given lines, is
Explanation for the correct option:
Step 1. Find the ratio in which origin divides the line:
Given
The equation of line perpendicular to and pass through the point is
Slope of (i) is
So, the slope of required equation, [Since, the lines are perpendicular]
So
Step 2. Solving (i) and (ii), to get intersection points
So the point of intersection of line (i) and (ii) is
Equation of second line is:
Point of intersection of (ii) and (iii) is
Step 3. Let the origin(0, 0) divides points of intersection of given lines and line in the ratio
Then
[Using section formula]
[Equating the coordinates]
The ratio is
Hence, option D is the answer.