Question

Need help with a math question

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

Answer:

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

Step-by-step 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)