If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are intersecting,

If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are intersecting, what is the nature of the intersection?

If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are intersecting, what is the nature of the intersection?

Step 1: Identify the given equation, which is 5x^2 + 6xy + 5y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y).
Step 3: Rewrite the equation in the standard form of a conic section to analyze it.
Step 4: Determine the coefficients: A = 5, B = 6, C = 5.
Step 5: Calculate the discriminant using the formula D = B^2 - 4AC.
Step 6: Substitute the values: D = 6^2 - 4(5)(5) = 36 - 100 = -64.
Step 7: Since the discriminant D is negative, this indicates that the conic section represents two intersecting lines.
Step 8: Find the slopes of the lines to determine the nature of their intersection.
Step 9: Calculate the slopes from the equation, which will show that the angle between the lines is obtuse.

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