Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
Practice Questions
1 question
Q1
Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
ab + h^2 = 0
ab - h^2 = 0
a + b = 0
a - b = 0
The condition for the lines to be perpendicular is given by the relation ab + h^2 = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
Solution: The condition for the lines to be perpendicular is given by the relation ab + h^2 = 0.
Steps: 5
Step 1: Understand that the equation ax^2 + 2hxy + by^2 = 0 represents two lines in a plane.
Step 2: Recognize that for two lines to be perpendicular, the product of their slopes must equal -1.
Step 3: The slopes of the lines can be derived from the coefficients a, b, and h in the equation.
Step 4: The condition for the lines to be perpendicular is derived mathematically and is expressed as ab + h^2 = 0.
Step 5: This means that if you know the values of a, b, and h, you can check if the lines are perpendicular by substituting them into the equation ab + h^2 = 0.
