Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.

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asked Jun 4, 2019 220k views

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Alvarado · Answer 1 · 2019-06-10T11:17:16+0000

so, we know the center is at -1, -3, hmmm what's the radius anyway?

well, the radius will be the distance from the center to any point on the circle, it just so happen that we know -7, -5 is on it, thus

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -1 &,& -3~) % (c,d) &&(~ -7 &,& -5~) \end{array} \\\\\\ d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ r=√([-7-(-1)]^2+[-5-(-3)]^2)\implies r=√((-7+1)^2+(-5+3)^2) \\\\\\ r=√(36+4)\implies r=√(40)\\\\ -------------------------------$

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{√(40)}{ r} \\\\\\\ [x-(-1)]^2+[y-(-3)]^2=(√(40))^2\implies (x+1)^2+(y+3)^2=40$

Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.

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