Respuesta :
The equation of the circle is [tex]x^2+y^2=25[/tex]
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,
[tex]Center=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Substituting the diameters of the circle (5,0) and (-5,0), we get,
[tex]Center=(\frac{5-5}{2},\frac{0-0}{2})[/tex]
[tex]Center=(0,0)[/tex]
Thus, the coordinates of the center is (0,0)
Radius:
The radius of the circle can be determined using the distance formula,
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Substituting the center (0,0) and one of the endpoints (5,0), we get,
[tex]r=\sqrt{(5-0)^2+(0-0)^2[/tex]
[tex]r=\sqrt{(5)^2+(0)^2[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex]
Thus, the radius of the circle is 5 units.
Equation of the circle:
The equation of the circle can be determined using the formula,
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where center = (h,k) = (0,0) and r = 5 units
Substituting, we get,
[tex](x-0)^2+(y-0)^2=5^2[/tex]
[tex]x^2+y^2=25[/tex]
Thus, the equation of the circle in standard form is [tex]x^2+y^2=25[/tex]
