Question

write the standard equation for the circle with the center at (4,1) and passing through the point (0,1)

Answer 1

Without needing the distance formula

from 4,1 to 0,1, you move the "x" from 4 to 0, over the same "y" value of 1, so is just 4 units long, from the center to an endpoint, and the chord that stems from the center to an endpoint is the radius, so r = 4

$\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &4&1&4 \end{array}$