Question: What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel?
Options:
h^2 = ab
h^2 > ab
h^2 < ab
h^2 = 0
Correct Answer: h^2 = ab
Solution:
The condition for the lines to be parallel is given by h^2 = ab.
What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be
Practice Questions
Q1
What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel?
h^2 = ab
h^2 > ab
h^2 < ab
h^2 = 0
Questions & Step-by-Step Solutions
What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel?
Correct Answer: h^2 = ab
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 parallel, they must have the same slope.
Step 3: The condition for the lines to be parallel can be derived from the coefficients of the equation.
Step 4: The condition is given by the formula h^2 = ab, where 'a', 'b', and 'h' are coefficients from the equation.
Step 5: If h^2 equals ab, then the two lines represented by the equation are parallel.
Conic Sections – Understanding the representation of conic sections, specifically the conditions under which the quadratic equation represents two lines.
Parallel Lines Condition – The specific mathematical condition (h^2 = ab) that determines when two lines represented by a quadratic equation are parallel.
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