The pair of lines represented by the equation x^2 - 4x + y^2 - 6y + 8 = 0 are:
Practice Questions
1 question
Q1
The pair of lines represented by the equation x^2 - 4x + y^2 - 6y + 8 = 0 are:
Parallel
Intersecting
Coincident
Perpendicular
To determine the nature of the lines, we can rewrite the equation in the form of (x - a)^2 + (y - b)^2 = r^2 and analyze the discriminant.
Questions & Step-by-step Solutions
1 item
Q
Q: The pair of lines represented by the equation x^2 - 4x + y^2 - 6y + 8 = 0 are:
Solution: To determine the nature of the lines, we can rewrite the equation in the form of (x - a)^2 + (y - b)^2 = r^2 and analyze the discriminant.
Steps: 8
Step 1: Start with the given equation: x^2 - 4x + y^2 - 6y + 8 = 0.
Step 2: Rearrange the equation to isolate the constant on one side: x^2 - 4x + y^2 - 6y = -8.
Step 3: Complete the square for the x terms (x^2 - 4x). To do this, take half of -4 (which is -2), square it (getting 4), and add it to both sides: (x - 2)^2 - 4.
Step 4: Complete the square for the y terms (y^2 - 6y). Take half of -6 (which is -3), square it (getting 9), and add it to both sides: (y - 3)^2 - 9.
Step 5: Substitute the completed squares back into the equation: (x - 2)^2 - 4 + (y - 3)^2 - 9 = -8.
