Question

Identify the equation of the circle that passes through (-3, -5) with center (4, -7).

a.) (x - 4)2 + (y + 7)2 = sqrt 53
b.) (x + 4)2 + (y - 7)2 = sqrt 53
c.) (x + 4)2 + (y - 7)2 = 53
d.) (x - 4)2 + (y + 7)2 = 53

Answer 1

what is the distance between the two given points?

Answer 2

I graphed it and came up with 7 as the distance? Most likely it could be wrong.

Answer 3

=(

Answer 4

unfortunately it is incorrect

Answer 5

you would use the distance formula to find the distance between the two points

are you familiar with that formula?

Answer 6

Yupp!

Answer 7

correct

Answer 8

ok great

Answer 9

so plug each point into the formula and show me what you get

Answer 10

I got the distance as the sqrt of 53

= 7.3

Is that okay?

Answer 11

perfect, that's the distance

Answer 12

so the radius is exactly \(\large r = \sqrt{53}\) units long

Answer 13

the center in general is (h,k)

so if the center is given to be (4, -7), then

(h,k) = (4, -7) ---> h = 4, k = -7

we now plug this all into \(\large (x-h)^2+(y-k)^2=r^2\) to get

\[\large (x-h)^2+(y-k)^2=r^2\]

\[\large (x-4)^2+(y-(-7))^2=(\sqrt{53})^2\]

\[\large (x-4)^2+(y+7)^2=53\]

which is the equation of the circle

Answer 14

Wow! Thank you so much! You are always very helpful! =)

Answer 15

I'm glad I am, yw