SOLUTION: A (9,5) and B (5,-9) are two points on a circle centered at the origin. a) Determine an equation for the circle. b) Determine the midpoint C of chord AB. c) Show that the

Question 1044109: A (9,5) and B (5,-9) are two points on a circle centered at the origin.
a) Determine an equation for the circle.
b) Determine the midpoint C of chord AB.
c) Show that the right bisector of chord AB passes through the centre of the circle.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^2+y^2=r^2
81+25=106 with point 1 and point 2.r=10.3
x^2+y^2=106 is the equation of the circle
The chord"s midpoint is the midpoint of each x and each y, or (7,-2)
The equation of the line that makes the chord has slope (-9-5)/(5-9)=-14/-4=7/2
the point slope formula is y+9=(7/2)(x-5), or y=(7/2)x-53/2.
The perpendicular bisector must have- slope -2/7, the negative reciprocal.
It's equation is y+2=(-2/7)(x-7), or y=(-2/7)x, and this goes through (0,0)

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