Question

F

Answer 1

Answer:

The equation of circle is $(x-8)^2+(y-4)^2=5$

(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

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Put the value into the formula

$d^2=(9-7)^2+(6-2)^2$

$d^2=20\ m$

The radius will be

$r^2=\dfrac{20}{4}$

$r^2=5$

We need to calculate the center of the point (7,2) and (9,6)

Using formula of center point

For x axis,

$h=\dfrac{x_{2}+x_{1}}{2}$

Put the value into the formula

$h=\dfrac{9+7}{2}$

$h=\dfrac{16}{2}$

$h=8$

For y axis,

$k=\dfrac{y_{2}+y_{1}}{2}$

Put the value into the formula

$k=\dfrac{6+2}{2}$

$k=\dfrac{8}{2}$

$k=4$

We need to find the equation for the circle

Using formula of equation of circle

$(x-h)^2+(y-k)^2=r^2$

Put the value into the formula

$(x-8)^2+(y-4)^2=5$

Hence, The equation of circle is $(x-8)^2+(y-4)^2=5$

(D) is correct option.