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Circle

Rayne Wooney

A point (-1,3) is on a circle with a radius of (square root of 20). If the centre of this circle is on the line x + y = 0, find the equations of the two possible circles.

Can anyone help me with this? The book I'm using only gives examples of this type of question when two points on the circle and the radius are given, this question only gives one point on the circle.

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TheBody

Rayne Wooney wrote: »

A point (-1,3) is on a circle with a radius of (square root of 20). If the centre of this circle is on the line x + y = 0, find the equations of the two possible circles.

Can anyone help me with this? The book I'm using only gives examples of this type of question when two points on the circle and the radius are given, this question only gives one point on the circle.

As per the charter, I can't just give you the solution but I'll try my best.

First thing to think about is the line that the centre lies on:

x+y=0

If we re-arrange this we get y=-x which looks like:

$3_6_Image4.gif$

Normally we denote the centre of a circle as (h,k). In our case, the centre is in the line above so we can say our centre must have coordinate (h,-h). We can now use the equation of a circle formula

[latex](x-h)^2+(y-k)^2=r^2[/latex]

with x=-1, y=3, h=h, k=-h and [latex]r^2=20[/latex] to solve for h.

(Hint: You should find two centres that work)

Rayne Wooney

Thanks for the help, can I just ask why it changes to h,h?

I got two answers h=10 and h=4?

TheBody

Rayne Wooney wrote: »

Thanks for the help, can I just ask why it changes to h,h?

I got two answers h=10 and h=4?

Sorry, I made a small mistake there. I should have had (h,-h). I edited my post above. As the centre lies along the line y=-x or x=-y, this is telling me that the x and y coordinates must only differ by a sign. Your answers are incorrect but that may be because I misled you above. Sorry about that!!

Rayne Wooney

TheBody wrote: »

Sorry, I made a small mistake there. I should have had (h,-h). I edited my post above. As the centre lies along the line y=-x or x=-y, this is telling me that the x and y coordinates must only differ by a sign. Your answers are incorrect but that may be because I misled you above. Sorry about that!!

So say if the line was x + y = 8 how would you go about doing the question?

I'll give it a go now with (h, -h), cheers

TheBody

Rayne Wooney wrote: »

So say if the line was x + y = 8 how would you go about doing the question?

I'll give it a go now with (h, -h), cheers

All I'm doing is writing the y coordinate in terms of x. I could do it the other way around either. So to answer your question above, I'd do the same thing only this time with y=-x+8. So instead of (h,k) we have (h,-h+8) and off we go again.