Question

The standard form of the equations of the circle is ?

Answer 1

The standard form of circle with center (a,b) and radius r.

`(x-a)^2+(y-b)^2=r^2`

In the given graph of circle, the center of circle is (4,3) and consider any one passing point let( 4,0)

Substitute x = 4, y = 0 and a = 4, b = 3 in the general equation of circle.

`\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (4-4)^2+(0-3)^2=r^2 \\ 0+3^2=r^2 \\ r=3 \end{gathered}`

Radius = 3

Substitute the center (a, b) = (4,3) and r=3

`\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-4)^2+(y-3)^2=3^2 \\ (x-4)^2+(y-3)^2=9 \end{gathered}`

The general equation of circle is

`(x-4)^2+(y-3)^2=9`