Question

The joint equation of bisectors of angles between lines x = 5 and y = 3 is ___________

A) (x – 5) (y – 3) = 0

B) x² – y² – 10x + 6y + 16 = 0

C) xy = 0

D) xy – 5x – 3y + 15 = 0

Answer 1

The equation of the line $$x=5$$ is a vertical line passing through $$(5,0)$$. The equation of the line $$y=3$$ is a horizontal line passing through $$(0,3)$$.

The angle between these two lines is $${90}^{\circ }$$, so the bisectors of the angles between them will be the lines passing through the point of intersection of the two given lines and bisecting the angles between them. The point of intersection of $$x=5$$ and $$y=3$$ is $$(5,3)$$.

The slope of the line $$x=5$$ is undefined, so the angle bisector passing through $$(5,3)$$ will be a horizontal line passing through $$(5,3)$$. Similarly, the slope of the line $$y=3$$ is 0 , so the angle bisector passing through $$(5,3)$$ will be a vertical line passing through $$(5,3)$$.

Therefore, the equation of the angle bisector passing through $$(5,3)$$ is $$x=5$$  and $$y=3$$, which can be written as $($x-5)(y-3)=0$$.Hence,theanswerisA)$$(x-5)(y-3)=0$$