Question

Finding equation of circle

Answer 1

Well, that is a good question..

To graph a circle, you need to know two things:

its center
+
its radius

And so if you even want to write down its equation



SO the center is gotten

for the radius, it could be calculated using the distance formula between the center and any point lies ON the circle (on the circumference)

Refer to the attached charts:

(-1,4)
(-4,2)$r= \sqrt{(-1-(-4))^2+(4-2)^2}= \sqrt{(-1+4)^2+(4-2)^2} \\~\\= \sqrt{3^2+2^2} = \sqrt{13}$

As we get the radius now, we are ready to plug it into the circle formula to get its equation...

$(x-(-4))^2+(y-2)^2=( \sqrt{13} )^2 \\~\\(x+4)^2+(y-2)^2=13$

And we are done now... :)