The equation of circle is: [tex]x^2+(y+2)^2 = 26[/tex]
Further explanation:
Standard form of equation is:
[tex](x-h)^2+(y-k)^2 = r^2\\[/tex]
Here (h,k) are the coordinates of the centre and r is radius.
As the centre and one point on boundary is given, we have to calculate the radius first.
Distance formula will be used to calculate radius.
[tex]d = r = \sqrt{x_2-x_1)^2+(y_2-y_1)^2}\\ = \sqrt{(-5-0)^2+(-1+2)^2}\\ =\sqrt{(-5)^2+(1)^2}\\ =\sqrt{25+1}\\ =\sqrt{26}[/tex]
Now
(h,k) = (0, -2)
Putting the values of r and (h,k) in standard equation
[tex](x-0)^2+(y-(-2))^2 = (\sqrt{26})^2\\(x)^2+(y+2)^2 = 26\\x^2+(y+2)^2 = 26[/tex]
The equation of circle is:
[tex]x^2+(y+2)^2 = 26[/tex]
Keywords: Equation of Circle, Radius of Circle
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