If the lines represented by the equation 4x^2 + 4xy + y^2 = 0 are coincident, wh

₹0.0

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

Options:

Correct Answer: 0

Solution:

The lines are coincident when the determinant of the coefficients is zero, leading to k = 0.

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

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

Step 1: Understand that the equation 4x^2 + 4xy + y^2 = 0 represents a pair of lines.
Step 2: Recognize that for the lines to be coincident, the determinant of the coefficients must be zero.
Step 3: Identify the coefficients from the equation: A = 4, B = 4, C = 1.
Step 4: Write the formula for the determinant: D = B^2 - 4AC.
Step 5: Substitute the values into the determinant formula: D = 4^2 - 4(4)(1).
Step 6: Calculate D: D = 16 - 16 = 0.
Step 7: Since D = 0, the lines are coincident, confirming that k = 0.

Coincident Lines – Coincident lines are lines that lie on top of each other, meaning they have the same slope and y-intercept.
Determinant of Coefficients – The determinant of the coefficients in a quadratic equation can be used to determine the nature of the roots, including whether the lines are coincident.