Question
Question: The straight line y = x–2 rotates about a point where it cuts the x-axis and becomes perpendicular t...
The straight line y = x–2 rotates about a point where it cuts the x-axis and becomes perpendicular to the straight line ax + by + c = 0. Then its equation is
A
ax + by + 2a = 0
B
ax – by – 2a = 0
C
bx + ay – 2b = 0
D
ay – bx + 2b = 0
Answer
ay – bx + 2b = 0
Explanation
Solution
Slope of the line in the new position is b/a, since it is perpendicular to the line ax + by + c = 0 and it cuts the x-axis. Hence the required line passes through (2, 0) and its slope is b/a. The required equation is y – 0 = b/a (x-2)
Or, ay = bx – 2b or, ay – bx + 2b = 0