Question

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

Answer 1

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)

Center:

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)

Radius:

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.

Equation of the circle:

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 $x^2+y^2=25$