Thread: [Coordinate Geometry] Locus

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 .

Thanks so much !

Originally Posted by CallMeBin

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 .

Thanks so much !

Let C be (x, y)
AC is perpendicular to BC
So slope of AC*slope of BC = -1.
Find the slopes of AC and BC and find the locus of C.

So the slope/gradient will be in unknown as C(x,y) ?

Originally Posted by CallMeBin

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 .

Thanks so much !

hi

OR

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 .

Originally Posted by CallMeBin

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 .

Thanks so much !

HI all
I think c will be any point belongs to the circle
(x-3)^2 + (y - 9/2)^2 = 65
except (-1 , 4) , (7 , 5 )
mrmohamed

Originally Posted by mathaddict

hi

OR

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 .

sorry mathaddict
I didnt see your post
mrmohamed

Thanks . I've done it . But I still don't understand why will it become like that (My way)

May I ask why = 65 ?

Originally Posted by CallMeBin

Thanks . I've done it . But I still don't understand why will it become like that (My way)

May I ask why = 65 ?

65 is the length of the diameter calculated using the distance formula .

@Mr Mohammad , no worries

Originally Posted by CallMeBin

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.

Thanks everyone !

This question is so special . The questions given by my teacher all are given the ratio but this one use distance instead of ratio .