If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the o

₹0.0

📥 Instant PDF Download
♾ Lifetime Access
🛡 Secure & Original Content

What’s inside this PDF?

Question: If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?

Options:

-1
0
1
2

Correct Answer: -1

Solution:

The product of the slopes of the lines can be found from the equation. Here, the product of the slopes is given by -c/a, where c is the coefficient of xy and a is the coefficient of x^2.

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the o

Practice Questions

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?

-1
0
1
2

Questions & Step-by-Step Solutions

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?

Correct Answer: -2/3

Step 1: Identify the given equation, which is 3x^2 + 2xy - y^2 = 0.
Step 2: Recognize that this equation represents two lines that intersect at the origin (0,0).
Step 3: Identify the coefficients in the equation: a = 3 (coefficient of x^2), c = 2 (coefficient of xy).
Step 4: Use the formula for the product of the slopes of the lines, which is -c/a.
Step 5: Substitute the values into the formula: -c/a = -2/3.
Step 6: Calculate the result: The product of the slopes is -2/3.

Quadratic Equations – Understanding how to analyze and factor quadratic equations to find the slopes of intersecting lines.
Slope of Lines – Knowledge of how to determine the slopes of lines represented by a quadratic equation.
Product of Slopes – Using the relationship between the coefficients of a quadratic equation to find the product of the slopes of the lines.

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the o

What’s inside this PDF?

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the o

Practice Questions

Questions & Step-by-Step Solutions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?