Question

Determine the equation of the circle graphed below

Answer 1

The equation would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.

Explanation:

Firstly, we need to find the radius of the circle. In this case, through the Pythagorean theorem, we can find it to be √(9-4)^2 + (4-3)^2 = √25 + 1 = √26.

Therefore, the equation of the circle would be (x – h)^2+ (y – k)^2 = r^2, where h and k are the x and y-coordinates of the center of the circle respectively, and r is the radius. Hence, the equation of this circle would be (x – 3)^2 + (y – 4)^2 = √26^2 or 26.

Hope this helped!

Answer 2

• (x - 3)² + (y - 4)² = 26

Explanation:

Equation in standard form:

• (x - h)² + (y - k)² = r²,

where (h, k) is the center and r- radius

On the graph we have (h, k) = (3, 4)

Find the r² using the distance formula:

• r² = ( 4 - 3)² + (9 - 4)² = 1² + 5² = 26

The equation is:

• (x - 3)² + (y - 4)² = 26