Question

Identify the equation for the circle with center (3, 7) that contains the point (9, 11).

Answer 1

Answer:

$(x-3)^2+(y-7)^2=2\sqrt{13}$

Step-by-step explanation:

The equation of a circle:

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

(h, k) - center

r - radius

We have the center (4, -3) and the point on the circle (9, -3).

The length of radius is equal to the distance between a center and an any point on a circle.

The formula of a distance between two points:

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

Susbtitute:

$r=\sqrt{(9-3)^2+(11-7)^2}\\\\=\sqrt{6^2+4^2}\\\\=\sqrt{52}\\\\=2\sqrt{13}$

The center (3, 7) → h = 3, k = 7.

Finally we have:

$(x-3)^2+(y-7)^2=2\sqrt{13}$