Answer:
[tex] {(x - 5)}^{2} + {(y - 4)}^{2} = 8 [/tex]
Step-by-step explanation:
Equation of circle can be written as
[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]
Here,r is radius and (a,b) is center of circle.
Given that circle is passing through ( 3,2 ) and center is ( 5,4 )
we can calculate radius r as
[tex] {r}^{2} = {( x_{1} - a)}^{2} + {( y_{1} - b)}^{2}[/tex]
[tex] {r}^{2} = {( 3 - 5)}^{2} + {( 2 - 4)}^{2} \\ {r}^{2} = 4 + 4 \\ {r}^{2} = 8[/tex]
Replacing values in equation of circle.
thus,
[tex] {(x - 5)}^{2} + {(y - 4)}^{2} = 8 [/tex]
