If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 are perpendicular

₹0.0

Question: If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 are perpendicular, what is the value of k?

Options:

Correct Answer: -1

Solution:

For the lines to be perpendicular, the condition 4 - 4(3)(2) = 0 must hold, leading to k = 0.

If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 are perpendicular, what is the value of k?

If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 are perpendicular, what is the value of k?

Step 1: Start with the given equation of the lines: 3x^2 + 4xy + 2y^2 = 0.
Step 2: Identify the coefficients in the equation: A = 3, B = 4, C = 2.
Step 3: Use the condition for perpendicular lines, which is given by the formula: B^2 - 4AC = 0.
Step 4: Substitute the values of A, B, and C into the formula: 4^2 - 4(3)(2).
Step 5: Calculate 4^2, which is 16.
Step 6: Calculate 4(3)(2), which is 24.
Step 7: Now, substitute these values into the equation: 16 - 24 = -8.
Step 8: Since the result is not zero, we need to adjust the coefficients to find the value of k that makes the lines perpendicular.
Step 9: Set the equation 4 - 4(3)(2) = 0 to find k.
Step 10: Solve for k, which leads to k = 0.

Quadratic Equations – Understanding the representation of lines through quadratic equations and their properties.
Perpendicular Lines – Condition for two lines to be perpendicular in terms of their slopes.
Discriminant Condition – Using the discriminant of a quadratic equation to determine the nature of the roots.