The circle x^2+(y-4)^2 = 25 intersects x-axis at points A and B . a point p lies on the major segment of the circle . the bisector of the angle APB for any point p can be given by the equation is?
answer = y = mx - 1
21Ans:Arcs(chords) of equal length subtend equal angles at the circumference.
The rest is simple calculations.
Take any pt on circle.Let the bisector of angle APB intersect circle at C.
Now for bisector,AC=BC
therefore C=(0,-1) [basic observation]
All bisectors pass through this pt,ie they have const y intercept.We can also infer that they have diff. slopes.
Therefore required equation is y=mx-1
21Have a look at the first statement.
Therefore if AC=BC,then angle subtended by AC at circumference=angle subtended at BC at circumference.
The only condition is that pt should not lie on arc AC or BC.That is why it is valid for pts on major segment only.
