Question

Currently needing to slove this problem

Answer 1

Check the picture below.

so it has a center at (2 , -5) and it passes through (4 , -4), now we could either the distance formula to get the "red" radius or just the pythagorean theorem, hmmm let's use the pythagorean theorem

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ c=√( 2^2 + 1^2)\implies c=√( 4 + 1 ) \implies c=√( 5 ) \\\\[-0.35em] \rule{34em}{0.25pt}`

`\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{-5}{k})}\qquad \stackrel{radius}{\underset{√(5)}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 2 ~~ )^2 ~~ + ~~ ( ~~ y-(-5) ~~ )^2~~ = ~~(√(5))^2\implies (x-2)^2 + (y+5)^2 = 5`