A(-1,4) and B(7,5) are two ends of the diameter of a circle . Find the equation of the locus of point C such that <ACB is a right angle .
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Use the phythagoras theorem . Let c be (x,y)
then simplify it , you will find the locus of c to be a circle because the point C can be any point on the circumference since the angle in the semicircle is a right angle .
then simplify it , you will find the locus of c to be a circle because the point C can be any point on the circumference since the angle in the semicircle is a right angle .
So the slope/gradient will be in unknown as C(x,y) ?
A(-1,4) and B(7,5)
Slope of AC = (y-4)/(x+1)
Slope of BC = (y-5)/(x-7)
They are perpendicular because ACB is a right angled triangle.So
(y-4)(y-5)/(x+1)(x-7) = -1.
After simplification you will get the locus of C.