Question

Determine the equation of the circle graphed below.screenshot is below - from delta math

Answer 1

Answer:

$\displaystyle \large{(x-5)^2+(y-2)^2=25}$

Step-by-step explanation:

Given:

• Center = (5,2)
• Endpoint = (8,6)

First, find radius via distance between center and endpoint. The formula of distance between two points is:

$\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

Determine:

• $\displaystyle \large{(x_1,y_1)=(5,2)}$
• $\displaystyle \large{(x_2,y_2)=(8,6)}$

Hence:

$\displaystyle \large{\sqrt{(8-5)^2+(6-2)^2}}\\\displaystyle \large{\sqrt{(3)^2+(4)^2}}\\\displaystyle \large{\sqrt{9+16} = \sqrt{25} = 5}$

Therefore, the radius is 5.

Then we can substitute center and radius in circle equation. The equation of a circle is:

$\displaystyle \large{(x-h)^2+(y-k)^2=r^2}$

Our center is at (h,k) which is (5,2) and radius beings 5.

Hence, your answer is:

$\displaystyle \large{(x-5)^2+(y-2)^2=25}$