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#1
A is the point ( 3,2 ) and B is the point (2,1). Find an equation for:

a) the circle on AB as a diameter
b) the circle that passes through A, B and the origin O.

0
14 years ago
#2
(Original post by Jackal123)
A is the point ( 3,2 ) and B is the point (2,1). Find an equation for:

a) the circle on AB as a diameter
b) the circle that passes through A, B and the origin O.

(a) You know that the centre of the circle is the midpoint of AB and that the radius is equal to half the distance AB. You can then put these values into the (x-a)^2 + (y-b)^2 = r^2 formula., where a,b correspond to the coordinates of the centre and r is obviously the radius.

(b) Multiply out the (x-a)^2 + (y-b)^2 = r^2 formulae and put the coordinates into the equation one at a time. You then have 3 equations and 3 unknowns so you can solve to find them.
0
#3
I still cant get the right answer. I get the midpoint to be (2.5, 1.5) and the radius to be 0.5

But the equation wont work!

Any help?
0
14 years ago
#4
(Original post by Jackal123)
I still cant get the right answer. I get the midpoint to be (2.5, 1.5) and the radius to be 0.5

But the equation wont work!

Any help?

0
14 years ago
#5
(Original post by Jackal123)
A is the point ( 3,2 ) and B is the point (2,1). Find an equation for:

a) the circle on AB as a diameter
b) the circle that passes through A, B and the origin O.

(a) The midpoint is (3+2)/2, (2+1)/2 = 2.5, 1.5
The diameter is rt[(1^2 + 1^2)]
The radius is (1/2)rt[2] = rt0.5

Using (x-a)^2 + (y-b)^2 = r^2
(x-2.5)^2 + (y-1.5)^2 = 0.5
You can also multiply this out to give:
x^2 - 5x + 5.0625 + y^2 - 3y + 2.25 = 0.5
x^2 + y^2 - 5x - 3y + 6.8125 =
16x^2 + 16y^2 - 80x - 48y + 109 = 0
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