Question: If the lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
Options:
a + b = 0
ab = h^2
a = b
h = 0
Correct Answer: a + b = 0
Solution:
For the lines to be perpendicular, the condition a + b = 0 must hold.
If the lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicula
Practice Questions
Q1
If the lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
a + b = 0
ab = h^2
a = b
h = 0
Questions & Step-by-Step Solutions
If the lines represented by the equation ax^2 + 2hxy + by^2 = 0 are perpendicular, then:
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, leading to the conclusion that a + b must equal 0.
Step 5: Therefore, if a + b = 0, the lines represented by the equation are perpendicular.
Condition for Perpendicular Lines – The condition for two lines represented by a quadratic equation to be perpendicular is derived from the coefficients of the equation.
Quadratic Forms – Understanding how the coefficients in a quadratic equation relate to the geometric properties of the lines it represents.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
