Answer:
[tex]n = - 4 \: or \: n = 8[/tex]
Step-by-step explanation:
If the point (2,n) lies on the circle whose equation is:
[tex]( {x - 4)}^{2} + {(y - 2)}^{2} = 40[/tex]
Then this point must satisfy the equation of the circle:
We substitute x=2 and y=n into the equation to get:
[tex]( {2 - 4)}^{2} + {(n - 2)}^{2} = 40[/tex]
We simplify:
[tex]4+ {(n - 2)}^{2} = 40[/tex]
This implies that,
[tex]{(n - 2)}^{2} = 40 - 4[/tex]
[tex] {(n - 2)}^{2} =36[/tex]
Take square root;
[tex]n - 2 = \pm \sqrt{36} [/tex]
Evaluate:
[tex]n - 2 = \pm6[/tex]
[tex]n =2 \pm6[/tex]
[tex]n =2 - 6 \: or \: n = 2 + 6[/tex]
[tex]n = - 4 \: or \: n = 8[/tex]
