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The locus of the equation xy = 0 is
- a)a pair of perpendicular lines
- b)a straight line
- c)a hyperbola
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The locus of the equation xy = 0 isa)a pair of perpendicular linesb)a ...
Xy=0
either x=0,y=some constant
or y=0,x=some constant
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either x=0,y=some constant
or y=0,x=some constant
so it will be a pair of perpendicular lines
Explanation :
Most Upvoted Answer
The locus of the equation xy = 0 isa)a pair of perpendicular linesb)a ...
Locus of the equation xy = 0 represents a pair of perpendicular lines.
Explanation:
To understand why the locus of the equation xy = 0 represents a pair of perpendicular lines, let's analyze the equation.
The equation xy = 0 can be rewritten as y = 0 or x = 0.
1. Locus of y = 0:
When y = 0, it means that the value of y is always 0, regardless of the value of x. This represents a horizontal line passing through the x-axis at y = 0. Since the value of y is fixed at 0, the line will be parallel to the x-axis.
2. Locus of x = 0:
When x = 0, it means that the value of x is always 0, regardless of the value of y. This represents a vertical line passing through the y-axis at x = 0. Since the value of x is fixed at 0, the line will be parallel to the y-axis.
Since the equation xy = 0 can be represented by the equations y = 0 and x = 0, it means that the locus of the equation consists of two lines: one horizontal line at y = 0 and one vertical line at x = 0.
As these two lines are perpendicular to each other (the horizontal line is parallel to the x-axis, and the vertical line is parallel to the y-axis), the locus of the equation xy = 0 represents a pair of perpendicular lines.
Hence, the correct answer is option A) a pair of perpendicular lines.
Explanation:
To understand why the locus of the equation xy = 0 represents a pair of perpendicular lines, let's analyze the equation.
The equation xy = 0 can be rewritten as y = 0 or x = 0.
1. Locus of y = 0:
When y = 0, it means that the value of y is always 0, regardless of the value of x. This represents a horizontal line passing through the x-axis at y = 0. Since the value of y is fixed at 0, the line will be parallel to the x-axis.
2. Locus of x = 0:
When x = 0, it means that the value of x is always 0, regardless of the value of y. This represents a vertical line passing through the y-axis at x = 0. Since the value of x is fixed at 0, the line will be parallel to the y-axis.
Since the equation xy = 0 can be represented by the equations y = 0 and x = 0, it means that the locus of the equation consists of two lines: one horizontal line at y = 0 and one vertical line at x = 0.
As these two lines are perpendicular to each other (the horizontal line is parallel to the x-axis, and the vertical line is parallel to the y-axis), the locus of the equation xy = 0 represents a pair of perpendicular lines.
Hence, the correct answer is option A) a pair of perpendicular lines.
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The locus of the equation xy = 0 isa)a pair of perpendicular linesb)a straight linec)a hyperbolad)none of theseCorrect answer is option 'A'. Can you explain this answer?
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