Determine the condition for the lines represented by the equation ax^2 + 2hxy +
Practice Questions
Q1
Determine the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
a + b = 0
ab = h^2
a - b = 0
h = 0
Questions & Step-by-Step Solutions
Determine the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
Correct Answer: a + b = 0
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 angle between them must be 90 degrees.
Step 3: Recall the condition for two lines represented by a quadratic equation to be perpendicular: it is given by the relationship between the coefficients a, b, and h.
Step 4: The specific condition for the lines to be perpendicular is that the sum of the coefficients a and b must equal zero, which can be written as a + b = 0.
Step 5: Therefore, if you find that a + b = 0, you can conclude that the lines are perpendicular.
Conic Sections – The equation ax^2 + 2hxy + by^2 = 0 represents a pair of lines, and understanding the conditions for their intersection and orientation is key.
Perpendicular Lines – Two lines are perpendicular if the product of their slopes is -1, which translates into a specific condition for the coefficients in the quadratic equation.
