Circle

[Raehya]

View attachment 33929

 

[BigBeachBanana]

Recall the formula for a circle.
[imath](x-h)^2+(y-k)^2=r^2[/imath], where [imath](h,k)[/imath] is the center of the circle and [imath]r[/imath] is the radius.
A point circle is a circle with a radius of [imath]0.[/imath]

Can you put the given equation into the standard formula of the circle? Once you've done that, set the RHS equal to 0 and solve for [imath]k.[/imath]

 

[Deleted member 4993]

Do you know the definition of "a point circle"?

Have you learned "how to complete a square"?

 

[Steven G]

To OP,
Although BigBeachBanana is correct about the general equation of a circle, I would replace the k used in the above post with say J simply because the letter k is already being used in your equation for something else.

 

[BigBeachBanana]

To OP,
Although BigBeachBanana is correct about the general equation of a circle, I would replace the k used in the above post with say J simply because the letter k is already being used in your equation for something else.

Nice catch, didn't even notice that.

 

[The Highlander]

View attachment 33931

While it is perfectly correct that: [imath](x-h)^2+(y-k)^2=r^2[/imath], where [imath](h,k)[/imath] is the center of the circle and [imath]r[/imath] is the radius is, indeed, the General Equation of a Circle (Though, in my country, we teach: "[imath](x-a)^2+(y-b)^2=r^2[/imath], where [imath](a, b)[/imath] is the center of the circle and [imath]r[/imath] is the radius"; which gets round the "problem" alluded to in the two posts just above this ?) it may be of more use to you to use the "Expanded Form" of the General Equation.

This may, therefore, be of some help to you…

​

 

[jonah2.0]

Beer induced reaction follows.

...
A point circle is a circle with a radius of [imath]0.[/imath] ...

Maybe I've one too many but I've always been uneasy about this description as it seems like an attempt to define the traditionally undefined element - the point.

 

[Otis]

in my country, we teach: (a,b) is the center of the circle and r is the radius"; which gets round the "problem" [of having symbol h or k already in use].

What if symbol a or b is already in use?

 

[The Highlander]

What if symbol a or b is already in use?

Then curiosity is called for.

 

[Otis]

it seems like an attempt to define the traditionally undefined element - the point.

Not to mention redefining the circle!
[imath]\;[/imath]

 

[Otis]

Then curiosity is called for.

Would that work also for h and k?

?
[imath]\;[/imath]

 

[The Highlander]

Would that work also for h and k?

?
[imath]\;[/imath]

Oh just delete my posts (rather than mangling them) if they offend you so much.
I'm done with you anyway!

 

[Steven G]

What if symbol a or b is already in use?

Come on Otis, the answer is obvious--just use h and k instead!