Show that the points P(5,5) and Q(6,2) lie on the circle
(x-1)sqr+(y-2)sqr=25
Show also that the perpendicular bisector of PQ goes through the centre.
Sketch: circle centre is (1, 2) and radius is 5.
To check if P and Q lie on the circle, substitute them into the circle equation.
at P(5,5) (x-1)sqr+(y-2)sqr=25 (5-1)sqr+(5-2)sqr=4sqr+3sqr= 25
at Q(6,2) (6-1)sqr+(2-2)sqr=5sqr+0sqr=25
The bisector of PQ cuts it in half.
Find the midpoint of PQ. Find the gradient of PQ. The gradient of the perpendicular to pq is 1/3
The perpendicular bisector of PQ goes through (11/2,7/2) with gradient 1/3
The equation is given by y-7/2=1/3(x-11/2) 3y-21/2=x-11/2 6y-21=2x-11 or 3y=x+5
Does the centre (1,2) lie on the line 3y=x+5?
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