find the equations of bisectors of angles between coordinate axes
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What is an Angle Bisector?
Angle bisector of two lines i.e. the line which bisects the angle between the two lines is the locus of a point which is equidistant from the two lines. In other words, an angle bisector has equal perpendicular distance from the two lines.
Suppose we have two lines
L1 : A1x + B1y + C1 = 0
L2 : A2x + B2y + C2 = 0
If point R(p, q) lies on the bisector, then length of perpendicular from the point R to both the lines should be equal.
Angle bisector of two lines i.e. the line which bisects the angle between the two lines is the locus of a point which is equidistant from the two lines. In other words, an angle bisector has equal perpendicular distance from the two lines.
Suppose we have two lines
L1 : A1x + B1y + C1 = 0
L2 : A2x + B2y + C2 = 0
If point R(p, q) lies on the bisector, then length of perpendicular from the point R to both the lines should be equal.
sonu1234555:
explain with diagram
i dont know how to send diagrm in comment box
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The equation of the coordinate axes are x = 0 and y= 0 and intersect at the origin (0,0).
The axes are perpendicular to each other and hence the angle between them is 90°. So, the bisector of the angle between the coordinate axes will be 45° and it will pass through the origin.
Thus , the required equation of the bisectors would be y = ±x ( Using y = mx , where m = tanθ and θ= 45°
The axes are perpendicular to each other and hence the angle between them is 90°. So, the bisector of the angle between the coordinate axes will be 45° and it will pass through the origin.
Thus , the required equation of the bisectors would be y = ±x ( Using y = mx , where m = tanθ and θ= 45°
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