Question: Find the condition for the lines represented by the equation 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.
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 parallel.
h^2 = ab
h^2 > ab
h^2 < ab
h^2 = 0
Questions & Step-by-Step Solutions
Find the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be parallel.
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: Recall that the condition for the lines to be parallel can be derived from the coefficients of the equation.
Step 4: The condition for the lines to be parallel is given by the formula h^2 = ab.
Step 5: This means that if you square the value of h and it equals the product of a and b, the lines are parallel.
Conic Sections – Understanding the representation of lines and their conditions in the context of conic sections, specifically the quadratic form.
Parallel Lines – Identifying the condition under which two lines represented by a quadratic equation are parallel.
Discriminant of Quadratic Forms – Applying the concept of the discriminant in the context of quadratic equations to determine the nature of the roots (lines).
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