Question: Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
Options:
ab + h^2 = 0
ab - h^2 = 0
a + b = 0
a - b = 0
Correct Answer: ab + h^2 = 0
Solution:
The condition for the lines to be perpendicular is given by the relation ab + h^2 = 0.
Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2
Practice Questions
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
Questions & Step-by-Step Solutions
Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
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.
Conic Sections – Understanding the representation of lines through quadratic equations and their geometric properties.
Perpendicular Lines – Condition for two lines to be perpendicular in the context of their slopes or coefficients.
Quadratic Forms – Analyzing the quadratic equation in two variables and its implications on the nature of the lines.
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