Respuesta :
Given:
Center of circle, (h, k) = (-10, -4)
Point the circle passes through ==> (4, -2)
Let's write the equation of the circle in standard form.
Apply the standard form of a circle equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
(h, k) is the radius.
r is the radius of the circle.
To find the radius, let's find the distance between the points using the distance between points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1})^2[/tex]Where:
(x1, y1) ==> (-10, -4)
(x2, y2) ==> (4, -2)
Thus, we have:
[tex]\begin{gathered} d=\sqrt{(4-(-10)^2+(-2-(-4))^2} \\ \\ d=\sqrt{(4+10)^2+(-2+4)^2} \\ \\ d=\sqrt{14^2+2^2} \\ \\ d=\sqrt{196+4} \\ \\ d=\sqrt{200} \\ \\ d=14.14 \end{gathered}[/tex]Hence, we have:
• Center, (h, k) = (-10, -4)
,• Radius of the circle = √200
Therefore, the equation of the circle is:
[tex]\begin{gathered} (x-(-10))^2+(y-(-4))^2=\sqrt{200^2} \\ \\ (x+10)^2+(y+4)^2=200 \end{gathered}[/tex]ANSWER:
[tex](x+10)^2+(y+4)^2=200[/tex]