If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 intersect at the

₹0.0

Question: If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 intersect at the origin, what is the angle between them?

Options:

Correct Answer: 90 degrees

Solution:

The angle can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes derived from the equation.

If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 intersect at the origin, what is the angle between them?

If the lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 intersect at the origin, what is the angle between them?

Correct Answer: 45 degrees

Step 1: Identify the given equation, which is 5x^2 + 6xy + 5y^2 = 0.
Step 2: Recognize that this is a quadratic equation in x and y, representing two lines that intersect.
Step 3: Rewrite the equation in the standard form of a conic section to find the slopes of the lines.
Step 4: Factor the equation or use the quadratic formula to find the slopes (m1 and m2) of the lines.
Step 5: Use the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)| to find the tangent of the angle θ between the two lines.
Step 6: Calculate the angle θ by taking the arctan of the value obtained in Step 5.

Quadratic Equations – Understanding how to interpret and manipulate quadratic equations to find slopes of lines.
Slopes of Lines – Calculating the slopes of intersecting lines from a quadratic equation.
Angle Between Lines – Using the formula for the angle between two lines based on their slopes.