Respuesta :
Answer:
The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
Step-by-step explanation:
Given that,
Points (6,5), (7,2), (9,6) and (10,3) are vertices of an inscribed square.
We need to calculate the distance between (7,2) and (9,6)
Using formula of distance
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Put the value into the formula
[tex]d^2=(9-7)^2+(6-2)^2[/tex]
[tex]d^2=20\ m[/tex]
The radius will be
[tex]r^2=\dfrac{20}{4}[/tex]
[tex]r^2=5[/tex]
We need to calculate the center of the point (7,2) and (9,6)
Using formula of center point
For x axis,
[tex]h=\dfrac{x_{2}+x_{1}}{2}[/tex]
Put the value into the formula
[tex]h=\dfrac{9+7}{2}[/tex]
[tex]h=\dfrac{16}{2}[/tex]
[tex]h=8[/tex]
For y axis,
[tex]k=\dfrac{y_{2}+y_{1}}{2}[/tex]
Put the value into the formula
[tex]k=\dfrac{6+2}{2}[/tex]
[tex]k=\dfrac{8}{2}[/tex]
[tex]k=4[/tex]
We need to find the equation for the circle
Using formula of equation of circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put the value into the formula
[tex](x-8)^2+(y-4)^2=5[/tex]
Hence, The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
