Explanation:
The equation of a circle with center (x1, y1) is:
[tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]Where r is the radius of the circle.
In this problem the equation is:
[tex](x+1)^2+(y-6)^2=r^2[/tex]To find the radius r we have to replace the coordinates of point A(4, -6) into the equation:
[tex]\begin{gathered} (4+1)^2+(-6-6)^2=r^2 \\ 5^2+12^2=r^2 \\ 25+144=r^2 \\ r^2=169 \end{gathered}[/tex]Therefore, the complete equation of this circle is:
[tex](x+1)^2+(y-6)^2=169[/tex]To find if point B(-6, 18) lies on the same circle we have to replace x = -6 and y = 18 into the equation above. If the equality is true, then the point lies on the circle:
[tex]\begin{gathered} (-6+1)^2+(18-6)^2=169 \\ (-5)^2+12^2=169 \\ 25+144=169 \\ 169=169\text{ --> true} \end{gathered}[/tex]Answer:
Point B lies on the same circle
