Question

A circle in the xy-plane is centered at (3, 0) and has a radius with endpoint (1, 8/3 ). Which answer choice is an equation of the circle?

Answer 1

Answer: (x - 3)² + y² = $\frac{100}{9}$

Step-by-step explanation:

Circle Formula: (x - h)² + (y - k)² = r²  ; (h, k) is the center & r is the radius

Use the distance formula for (3, 0) and (1, $\frac{8}{3}$)

$r = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

$r = \sqrt{(3-1)^{2}+(0-\frac{8}{3})^{2}}$

$r = \sqrt{(2)^{2}+(-\frac{8}{3})^{2}}$

$r = \sqrt{4+\frac{64}{9}}$

$r = \sqrt{\frac{36}{9}+\frac{64}{9}}$

$r = \sqrt{\frac{100}{9}}$

$r = \frac{10}{3}$

****************************************************

Center (h, k) = (3, 0)   Radius (r) = $\frac{10}{3}$

(x - h)² + (y - k)² = r²

(x - 3)² + (y - 0)² = ($\frac{10}{3}$)²

(x - 3)² + y² = $\frac{100}{9}$