# Equation of the circle.Write the circle equation if it passes through the point (5,4) and the center of circle is (2,0).

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### 2 Answers

The distance between the point (5,4) and (2,0) is sqrt(9 + 16) = 5

As the center of the circle is (2,0) and the point (5,4) lies of it, the distance between the points is equal to the radius.

The equation of the circle is (x - 2)^2 + (y - 0)^2 = 25

=> x^2 - 4x + 4 + y^2 = 25

=> x^2 + y^2 - 4x - 21 = 0

**The equation of the circle is x^2 + y^2 - 4x - 21 = 0**

We'll write the equation of the circle:

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

The center of the circle has the coordinates C(h ; k).

We know, from enunciation, that h = 2 and k = 0.

We'll substitute them into the equation:

(x - 2)^2 + (y - 0)^2 = r^2

We'll determine the radius considering the constraint from enunciation that the circle is passing through the point (5,4).

If the circle is passing through the point (5,4), then the coordinates of the point are verifying the equation of the circle:

(5 - 2)^2 + (4 - 0)^2 = r^2

3^2 + 4^2 = r^2

9 + 16 = r^2

25 = r^2

r = 5

Note: we remark that 3,4 are the pythagorean numbers, so the radius could only be 5.

**The equation of the circle is:**

**(x - 2)^2 + (y)^2 = 25**