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If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the o
If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?
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Practice Questions
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Q1
If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?
-5/6
5/6
1
0
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The sum of the slopes of the lines is given by -b/a, which is 0 in this case.
Questions & Step-by-step Solutions
1 item
Q
Q: If the lines represented by the equation 6x^2 + 5xy + y^2 = 0 intersect at the origin, what is the sum of their slopes?
Solution:
The sum of the slopes of the lines is given by -b/a, which is 0 in this case.
Steps: 6
Show Steps
Step 1: Identify the given equation, which is 6x^2 + 5xy + y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y) that can represent two lines.
Step 3: Rewrite the equation in the standard form of a quadratic equation: Ax^2 + Bxy + Cy^2 = 0, where A = 6, B = 5, and C = 1.
Step 4: Use the formula for the sum of the slopes of the lines represented by the equation, which is -B/A.
Step 5: Substitute the values of B and A into the formula: -B/A = -5/6.
Step 6: Calculate the result: -5/6 is the sum of the slopes of the lines.
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