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lee1111 · Mar 6, 2011, 12:51 AM

The equation of a diameter of a circle passing through the origin is x + y = 1 and th

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the equation of diameter of a circle passing through the origin is x y=1 and the greatest distance of any point of the circle from the diameter is (5)^1/2.then the equation of the circle is?

galactus · Mar 6, 2011, 10:15 AM

Didn't you preview your problem before posting? It appears to be cut off?

Do you need the equation of a circle whose diameter is the line x+y=1?

There could be many circles with radius on this line, but say you want one that passes through
(1,0) and (0,1).

The line y=-x+1 crosses the x-axis at (1,0) and the y-axis at (0,1).

The distance between these two points is then $\sqrt{2}$

This is the length of the circles diameter. Thus, the radius is $\frac{\sqrt{2}}{2}$

By using the midpoint formula, we find the circle has center $(\frac{1}{2}, \;\ \frac{1}{2})$

Now, there's the center and radius, write out the equation.

$(x-\frac{1}{2})^{2}+(y-\frac{1}{2})^{2}=(\frac{\sqrt{2}}{2})^{2}$

Unknown008 · Mar 7, 2011, 08:58 AM

The general equation of a circle is:

$(x - a)^2 + (y - b)^2 = r^2$

where (a, b) is the coordinates of the centre of the circle and r is the radius of the circle.

As you can see, this is similar to the equation that galactus posted above, but with a = 1/2, b = 1/2 and r = \sqrt{2}/2.

Can you give your problem a try?

lee1111 · Mar 8, 2011, 11:21 AM

I tried to solve the problem but I am not getting the correct answer... :(
Its given that greatest distance of any point of the circle from the diameter is root 5

Unknown008 · Mar 8, 2011, 12:26 PM

What answer did you come to?