Question

A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?

Answer 1

(-6, 4)
(2, -1)
(-4, -4)
(2, -9)

Answer 2

do you know the standard form equation of the circle ?

Answer 3

Do you mean the distance?

Answer 4

yes same equation for both

Answer 5

Yyeah, I can't understand how to calculate that, I do know the d formula tho ;v;

Answer 6

well the standard form equation of the circle is \[\huge\rm (x-h)^2 +(y-k)=r^2\] where (h,k) is the center and
r = radius

Answer 7

use the formula area of a circle \[\huge\rm A= \pi r^2\] to find r (radius )

Answer 8

is (y-k) also supposed to be ^2? So is h=2 and k=4??

Answer 9

yes right forgot sorry about that \[\huge\rm (x-h)^2 +(y-k)^2=r^2\]

Answer 10

yes right h=2 k =4

Answer 11

And I should just try each of the options until one of them is 78.5...?

Answer 12

@Nnesha ?

Answer 13

thanks for tag i was afk alright first you need to find the radius

Answer 14

the given is 78.5 area so substitute a for 78.5 and then solve for r

Answer 15

a?

Answer 16

what do you mean ?

Answer 17

use the formula area of a circle \[\huge\rm A= \pi r^2\] to find radius

Answer 18

Oohhhh 78.5=pir^2 Umm, I assume I divide pi from both sides then?

Answer 19

yes right

Answer 20

25 o.o

Answer 21

So I do 3.14*25^2?

Answer 22

yes r^2 equal 25 yes right forgot sorry about that \[\huge\rm (x-2)^2 +(y-4)^2=25\]
now you can substitute (x,y) for each order pair if you get equal sides then that order pair would be the answer

Answer 23

no we need r^2 which is 25
you can check your work 3.14*25^2 iif its equal 78.5 then 25 is correct

Answer 24

It isn't equal to 78.5 .-.

Answer 25

r^2 =25 not r=
so dont' take square of 25

Answer 26

\[\huge\rm \frac{ 78.5 }{ 5 }=r^2 ~~~~----> 25=r^2\] to find r you should take square root but we need r^2 for the equation

Answer 27

Ooh Okay, then yeah it's right--so then I just try each of the answers in the slots for x and y until I get the right one?

Answer 28

yep!

Answer 29

Oh okay! I already know the correct answer which is (2,-1) and I tested it and it's right! Thanks so much!! :)

Answer 30

np :=)goood work!