I've watched too many videos but I couldn't figure out how to solve it. Can someone help me??

@Raehya

Completing the square is a perfectly valid approach, when a circle's equation is given in the "Expanded Form"
\(\displaystyle x^2+y^2+2gx+2fy+c=0\).
​
The centre's coordinates can be read (almost) directly from the equation, and we can calculate the radius using a simple formula: \(\displaystyle \left(\sqrt{g^2+f^2–c}\right)\).

At least that is the way it is taught here in Scotland (and, I believe, throughout the rest of the UK too; other countries may differ in their approaches, of course).

Please watch this video.
(It won't hurt to watch just one more video, especially if it directly addresses your problem!)

This is another 'lesson' prepared with Scottish Higher Maths students in mind (by another Scottish Maths teacher) and the very first screen explains everything you need to know but, if you persevere and watch all the way through the examples provided, the third example shows you exactly how to solve your particular problem.

Hope that helps.

PS: If you decide to jump in without watching the examples, please be sure to follow @Steven G's advice:-
Steven G said:
1st divide all terms by 4.
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because, as the video's first screen explains, the \(\displaystyle x^2\) & \(\displaystyle y^2\) coefficients must both be 1 (for the method to "work"!) However, I strongly advise you to watch at least the first three examples provided in the video and, at the very least, study the third example if no others.
 
I've watched too many videos but I couldn't figure out how to solve it.
Can someone help me??
Click to expand...

Hello Raehya. What kind of help do you need? Do you have any specific questions about what you've seen in prior videos or how their explanations apply to your exercise?

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BigBeachBanana said:
I believe there's an error in your formula. It should be minus [imath]c[/imath].
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You are absolutely right! I should, indeed, have typed: \(\displaystyle \left(\sqrt{g^2+f^2\textcolor{red}{-c}}\right)\); my bad! ?

The video that I have directed the OP to does not, of course, have the same error in it and makes it clear that the correct formula for the radius is: \(\displaystyle \left(\sqrt{g^2+f^2-c}\right)\)

However, watching the video myself, I note that the speaker does make a slight boob almost at the end of the first slide when he says: "So, \(\displaystyle g^2+f^2-c\) must equal zero in order for it to be a circle" when he clearly meant to say: "... must be greater than zero in order for it to be a circle"! ?

I guess we all make (small?) mistakes occasionally but thanks for pointing that out @BigBeachBanana. ??
 
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