The equation of the circle will be [tex]x^2+(y-5)^2=25[/tex]
The formula finding the equation of a circle is expressed as:
[tex](x-a)^2+(y-b)^2=r^2[/tex] where:
r is the radius of the circle
(a, b) is the center
Given the centre (0, 5)
Get the radius
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\r=\sqrt{(0-0)^2+(0-5)^2}\\r=\sqrt{25}\\r=5units[/tex]
Substitute the radius and the centre into the equation of a circle as shown:
[tex](x-0)^2+(y-5)^2=5^2\\x^2+(y-5)^2=25[/tex]
This gives the equation of the circle.
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The equation of the circle is [tex]x^2 + (y-5)^2 = 25[/tex]
The graph of the circle is plotted below
The equation of a circle is of the form:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
where (a, b) is the center of the circle
In this question:
The center, (a, b) = (0, 5)
The radius is the distance between (0, 5) and (0, 0)
Find the distance using the formula below
[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance = \sqrt{(0-0)^2+(0-5)^2}\\Distance = \sqrt{25}\\Distance = 5[/tex]
The radius = 5
Substitute a = 0. b = 5, and r = 5 into the equation of a circle
[tex](x - a)^2 + (y - b)^2 = r^2\\\\(x - 0)^2 + (y - 5)^2 = 5^2\\\\x^2 + (y-5)^2 = 25\\[/tex]
The equation of the circle is
[tex]x^2 + (y-5)^2 = 25[/tex]
The graph of the circle is plotted below
Learn more here: https://brainly.com/question/23226948
