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Determine the equation of the circle graphed below.

screenshot is below - from delta math

Determine the equation of the circle graphed below. screenshot is below - from delta-example-1
User Viliamm
by
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1 Answer

9 votes

Answer:


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

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

User Fergie
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