Question

Question is attached

Find the equation of following attachment ​

Answer 1

ANSWER :

${(x + 1)}^{2} + {(y - 7)}^{2} = 8$

EXPLANATION :

The given circle has P(-3,5) and Q(1,9) as its diameter.

The center can be obtained using the midpoint rule.

$( \frac{ - 3 + 1}{2} , \frac{5 + 9}{2} )$

$( - 1,7)$

The radius is obtained using the distance formula,

$r = \sqrt{( - 1 - (- 3 ))^{2} + {(7 - 5)}^{2} }$

$r = \sqrt{( 2)^{2} + {(2)}^{2} } = \sqrt{8}$

The equation is given by

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

We substitute the center and radius to get:

${(x - ( - 1))}^{2} + {(y - 7)}^{2} = { (\sqrt{8}) }^{2}$

${(x + 1)}^{2} + {(y - 7)}^{2} = 8$

Answer 2

The given circle has P(-3,5) and Q(1,9) as its diameter.

The center can be obtained using the midpoint rule.

The radius is obtained using the distance formula,

The equation is given by

We substitute the center and radius to get: