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ra1l [238]
2 years ago
7

Write the equation in standard form for the circle that has a diameter with endpoints (5,0) and (–5,0).

Mathematics
1 answer:
Zanzabum2 years ago
6 0

The equation of the circle is x^2+y^2=25

Explanation:

Given that the endpoints of the circle.

The coordinates of the endpoints are (5,0) and (-5,0)

<u>Center:</u>

The center of the circle can be determined using the midpoint formula,

Center=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Substituting the diameters of the circle (5,0) and (-5,0), we get,

Center=(\frac{5-5}{2},\frac{0-0}{2})

Center=(0,0)

Thus, the coordinates of the center is (0,0)

<u>Radius:</u>

The radius of the circle can be determined using the distance formula,

r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Substituting the center (0,0) and one of the endpoints (5,0), we get,

r=\sqrt{(5-0)^2+(0-0)^2

r=\sqrt{(5)^2+(0)^2

r=\sqrt{25}

r=5

Thus, the radius of the circle is 5 units.

<u>Equation of the circle:</u>

The equation of the circle can be determined using the formula,

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

where center = (h,k) = (0,0) and r = 5 units

Substituting, we get,

(x-0)^2+(y-0)^2=5^2

                 x^2+y^2=25

Thus, the equation of the circle in standard form is x^2+y^2=25

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