Question

A circle has a center (3, 5) and the point (4, -3) on the circumference.

1. Find the radius of the circle.

2. Write an equation of the circle in standard form.

Answer 1

$\textsf{1.}$

$\textsf{To find the radius of the circle is necessary to calculate the distance of the }\\\textsf{points (3, 5) and (4, -3).}$

$\textsf{So:}$

$\mathsf{r = \sqrt{(\Delta x)^2 +( \Delta y)^2} = \sqrt{(4 - 3)^2 + (-3 -5)^2} = \sqrt{1^2 + 8^2} = \sqrt{65}}\textsf{ where r is} \\ \textsf{radius of the circle.}$

$\textsf{2.}$

$\textsf{The equation of the circle is:}\\\mathsf{(x - a)^2 + (x - b)^2 = r^2} \textsf{ where (a, b) are the coordinates fo the center of the}\\\textsf{circle}$

$\textsf{Hence the equation of the circle with center (3, 5) that passes for (4, -3) is:}\\\mathsf{(x - 3)^2 + (y - 5)^2 = 65}$