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For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum
For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?
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Practice Questions
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Q1
For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?
-5/6
5/6
0
1
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The sum of the slopes of the lines is given by -b/a, which is -5/6.
Questions & Step-by-step Solutions
1 item
Q
Q: For the lines represented by the equation 6x^2 + 5xy + y^2 = 0, what is the sum of the slopes?
Solution:
The sum of the slopes of the lines is given by -b/a, which is -5/6.
Steps: 7
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).
Step 3: Rewrite the equation in the standard form of a conic section, which is Ax^2 + Bxy + Cy^2 = 0.
Step 4: Identify the coefficients: A = 6, B = 5, C = 1.
Step 5: Use the formula for the sum of the slopes of the lines represented by the equation, which is -B/A.
Step 6: Substitute the values of B and A into the formula: -5/6.
Step 7: Conclude that the sum of the slopes of the lines is -5/6.
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