Question: The lines represented by the equation 5x^2 - 6xy + y^2 = 0 intersect at which point?
Options:
(0,0)
(1,1)
(2,2)
(3,3)
Correct Answer: (0,0)
Solution:
The lines intersect at the origin, which can be verified by substituting x = 0 and y = 0 into the equation.
The lines represented by the equation 5x^2 - 6xy + y^2 = 0 intersect at which po
Practice Questions
Q1
The lines represented by the equation 5x^2 - 6xy + y^2 = 0 intersect at which point?
(0,0)
(1,1)
(2,2)
(3,3)
Questions & Step-by-Step Solutions
The lines represented by the equation 5x^2 - 6xy + y^2 = 0 intersect at which point?
Step 1: Understand that the equation 5x^2 - 6xy + y^2 = 0 represents two lines.
Step 2: To find the intersection point of these lines, we can substitute x = 0 and y = 0 into the equation.
Step 3: Substitute x = 0 into the equation: 5(0)^2 - 6(0)(y) + y^2 = 0, which simplifies to y^2 = 0.
Step 4: Solve y^2 = 0, which gives y = 0.
Step 5: Now we have x = 0 and y = 0, so the intersection point is (0, 0).
Quadratic Equations – The question involves solving a quadratic equation in two variables to find the intersection points of the lines it represents.
Intersection of Lines – Understanding how to find the intersection points of lines represented by a quadratic equation.
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