what is the standard equation of a circle with center (-2, 6) that passes through the point (-2,10)?

Question

akashdeepdeb · Answer

Do you know the equation of a circle?

anonymous · Answer

I don't know anything. I'm a writer not a math person

jollypikachu300 · Answer

im not really good with math @Scenequeen26 if u asked me to do spelling i could do it

anonymous · Answer

if you do not know the standard form of the equation for a circle, there is no way to even begin to answer this question
surely it is in your text book, or a quick google search will find it 
but you need that first

anonymous · Answer

@Scenequeen26 
Feeling neglected? ^^

anonymous · Answer

@Supreme_Kurt yes i am lol

anonymous · Answer

Well then, the equation of a circle looks like this... and since you're a writer, I'm confident you won't be intimidated by the presence of so many letters XD

$$\Large (x - \color{red}h)^2 + (y-\color{green}k)^2 = \color{blue}r^2$$

Ready to start?

anonymous · Answer

yeah I'm ready

anonymous · Answer

I hope you're not colourblind :P

What we're going to do here is replace all those coloured letters with their appropriate numbers.  

For starters, let's pick the the easy bit. h and k.
$\Large (\color{red}h \ , \ \color{green}k)$  is the centre of the circle, and this has already been identified in your question.  What is h, and what is k? ^^

anonymous · Answer

-2 and 10

anonymous · Answer

Why? ^^

anonymous · Answer

-2, 6 I read the wrong one

anonymous · Answer

Good that you caught that ^^.
So after replacing h and k accordingly, our equation now becomes...?

anonymous · Answer

$$(x+2)^{2} + (y-6)^{2} = r ^{2}$$

anonymous · Answer

Now we just have to find r. The Radius.
Also known as how far from the center to the actual circle.  Your thoughts?

anonymous · Answer

I don't know to be honest.

anonymous · Answer

Well, we COULD (and will, obviously) get the distance FROM the center TO a point which we know for a fact is on the circle.  That point is (-2, 10)

How far from (-2 , 6) to (-2, 10) ?

anonymous · Answer

(0,2)???? maybe?

anonymous · Answer

A distance, m'lady (HAHA)
A distance is what we seek.  
A simple number, it is, and find it we shall.

You could use the distance formula here.  OR you could note that since both x-values of (-2 , 6) and (-2 , 10) are -2, you could just get the difference of their y-values.  And that difference is...?