The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel

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Question: The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:

Options:

Correct Answer: h^2 = ab

Solution:

The lines are parallel if h^2 = ab.

The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:

The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:

Step 1: Understand that the equation ax^2 + 2hxy + by^2 = 0 represents two lines.
Step 2: Recognize that for two lines to be parallel, their slopes must be equal.
Step 3: Recall that the condition for the lines to be parallel can be derived from the coefficients of the equation.
Step 4: The condition for parallel lines in this case is given by the formula h^2 = ab.
Step 5: Therefore, if you have values for a, b, and h, you can check if h^2 equals ab to determine if the lines are parallel.

Conic Sections – Understanding the conditions under which the quadratic equation represents lines and their relationships.
Parallel Lines – Identifying the mathematical condition for two lines to be parallel based on their coefficients.