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Locus of a point P equidistant from two fixed points A and B is ____________
- a)an ellipse
- b)a line perpendicular to AB passing through the midpoint of AB
- c)a circle with AB as largest chord
- d)a parallel line of AB
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Locus of a point P equidistant from two fixed points A and B is ______...
The line which makes equal distance from the two fixed points will definitely pass through the midpoint of line joining the two points and will definitely perpendicular to the line formed by joining the two points.
Most Upvoted Answer
Locus of a point P equidistant from two fixed points A and B is ______...
Explanation:
Definition of Locus:
The locus of a point is the set of all points that satisfy a particular condition or set of conditions.
Equidistant from Points A and B:
When a point P is equidistant from two fixed points A and B, it means that the distances from point P to points A and B are equal. This forms the basis of the locus of point P.
Line Perpendicular to AB:
Since point P is equidistant from points A and B, the locus of point P will be a line that is perpendicular to the line segment AB and passes through the midpoint of AB. This is because the shortest distance between a point and a line is a perpendicular line from the point to the line.
Midpoint of AB:
The midpoint of AB is the point that divides the line segment AB into two equal parts. Any point equidistant from A and B must lie on the perpendicular bisector of AB, which passes through the midpoint of AB.
Conclusion:
Therefore, the locus of a point P that is equidistant from two fixed points A and B is a line that is perpendicular to AB and passes through the midpoint of AB. This can be visualized as a line that divides the line segment AB into two equal parts.
Definition of Locus:
The locus of a point is the set of all points that satisfy a particular condition or set of conditions.
Equidistant from Points A and B:
When a point P is equidistant from two fixed points A and B, it means that the distances from point P to points A and B are equal. This forms the basis of the locus of point P.
Line Perpendicular to AB:
Since point P is equidistant from points A and B, the locus of point P will be a line that is perpendicular to the line segment AB and passes through the midpoint of AB. This is because the shortest distance between a point and a line is a perpendicular line from the point to the line.
Midpoint of AB:
The midpoint of AB is the point that divides the line segment AB into two equal parts. Any point equidistant from A and B must lie on the perpendicular bisector of AB, which passes through the midpoint of AB.
Conclusion:
Therefore, the locus of a point P that is equidistant from two fixed points A and B is a line that is perpendicular to AB and passes through the midpoint of AB. This can be visualized as a line that divides the line segment AB into two equal parts.
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Locus of a point P equidistant from two fixed points A and B is ____________a)an ellipseb)a line perpendicular to AB passing through the midpoint of ABc)a circle with AB as largest chordd)a parallel line of ABCorrect answer is option 'B'. Can you explain this answer?
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