I need help finding the equation of a circle (Pre-Calculus)?

Question

my teacher gave us this problem and i'm having trouble understanding what to do.

"find the equation of a circle with a center at (1,3) and a point at (3,4)"

i have a formula:

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

and i know to plug the values into it:

(3-1)^2+(4-3)^2=r^2

but i don't know if i should solve down to r or not.

Answer 1

The equation (x - h)^2 + (y - k)^2 = r^2 represents a circle of radius r centred at (h, k).

A circle centered at (1, 3) has an equation:

(x - 1)^2 + (y - 3)^2 = r^2.

You know the circle passes through (3, 4). As its centre is (1, 3), the radius r is the distance between these two points, and r^2 is the square of this distance.

From Pythagoras' Theorem:

r^2 = (4 - 3)^2 + (3 - 1)^2

= 1^2 +  2^2

= 1 + 4

= 5.

The equation is therefore:

(x - 1)^2 + (y - 3)^2 = 5.