Question

Need help with a math question

Answer 1

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

Explanation:

You should try the next one and I can check work or tell you if it is right.

The diameter length can be found be computing the distance that (-3,5) is to (1,9) which is sqrt(4^2+4^2)=sqrt(32).

The radius is half the diameter so it is sqrt(32)/2.

The center of the circle is the midpoint of a diameter. So compute the (Average of x, average of y)=(-1,7)

So plug into (x-h)^2+(y-k)^2=r^2 we get

(x+1)^2+(y-7)^2=32/4

simplifying gives

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

(I had to type this twice; my cat jump on my keyboard)

Answer 2

`{(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.

`( ( - 3 + 1)/(2) , (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) } = √(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) = { (√(8)) }^(2)`

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