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Jackal123
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#1
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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.

Please can someone help me! Thanks in advance
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Gaz031
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#2
Report 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.

Please can someone help me! Thanks in advance
(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.
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Jackal123
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#3
Report Thread starter 14 years ago
#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?
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Fermat
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#4
Report 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?
Check your arithmetic

Radius shoud be rt(0.5).
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Gaz031
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#5
Report 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.

Please can someone help me! Thanks in advance
(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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