Question

Write the equation of the circle with center (3, 2) and with (9, 3) being a point on the circle.

Answer 1

The equation of a circle:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - center

r - radius

We have the center (3, 2) → h = 3 and k = 2.

The length of a radius is equal a distance between a center and a point (9, 3).

The formula of a distance:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute:

$r=\sqrt{(3-2)^2+(9-3)^2}=\sqrt{1^2+6^2}=\sqrt{1+36}=\sqrt{37}$

Substitute to the equation of a circle:

$(x-3)^2+(y-2)^2=(\sqrt{37})^2\\\\\boxed{(x-3)^2+(y-2)^2=37}$