Question

given a circle whose equation is x^2 +8x+y^2-4y=5 determine the equation of the circle that is translated to the right 4 units and up 2 units that has an area which is twice that of the given circle

Answer 1

this may actually go under geometry, but it was one of my precal questions so I'm not sure

Answer 2

so pretty much to get the Area of any circle all you need is the "radius"
so in short, once you get the radius of the GIVEN circle, you'd get its Area

double that Area, will equal \(\bf \large \pi r^2\) in the other circle, solve for "r" to get the radius of it
once you have its radius, you have the equation, notice that (h, k) are given

Answer 3

"translated to the right 4 units and up 2 units" <---- (h, k)

Answer 4

so, all you really need is the radius

Answer 5

"translated to the right 4 units and up 2 units" => \(\bf (x+4)^2+(y-2)^2 = r^2\)

Answer 6

but how do I find the radius of the given circle? do i have to graph it??

Answer 7

you complete the square, to get the equation

Answer 8

of the origional equation or the one you just wrote?

Answer 9

\(\bf x^2 +8x+y^2=5\)

Answer 10

ok hold on i got this

Answer 11

did you drop the -4y on purpose?

Answer 12

"given a circle whose equation is x^2 +8x+y^2=5 determ...." <--- is the posting

Answer 13

shoot! sorry let me fix that

Answer 14

ok no sorry. its x^2 +8x+y^2-4y=5

Answer 15

ok

Answer 16

(x+4)^2 (y-2)^2=25

Answer 17

yes, that'd be the circle, and its Area = \(\bf 2 \pi r^2\)

Answer 18

r = 25?

Answer 19

\(\bf r^2 = 25 \implies r = 5\)

Answer 20

50 pi

Answer 21

yes

Answer 22

\(\bf r = 5\qquad \qquad Area = 2 \pi r^2 \implies Area = 50\pi\\
\textit{area of the other circle is double that } 100\pi \textit{thus }\\
100\pi = \pi r^2 \implies \sqrt{\cfrac{100\cancel{\pi}}{\cancel{\pi}} }= r\)

Answer 23

"translated to the right 4 units and up 2 units" => \(\bf (x+4)^2+(y-2)^2 = r^2 \implies (x+4)^2+(y-2)^2 = 10^2\)

Answer 24

thank you so much! if i could give you another medal I would!

Answer 25

yw

Answer 26

hmnmmm

Answer 27

one sec ... .... I have.. one thing amiss

Answer 28

I used above \(\bf 2\pi r^2 \) for the area which is only \(\bf \pi r^2\)

Answer 29

so instead of 10 is it 5?

Answer 30

or is all of it wrong now?

Answer 31

nope, gimme one sec

Answer 32

\(\bf r = 5\qquad \qquad Area = \pi r^2 \implies Area = 25 \pi\\
\textit{area of the other circle is double that } 50\pi \textit{ thus }\\
50 \pi = \pi r^2 \implies \sqrt{\cfrac{50\cancel{\pi}}{\cancel{\pi}} }= r \implies r = \sqrt{50}\)

Answer 33

"translated to the right 4 units and up 2 units" =>
\(\bf (x+4)^2+(y-2)^2 = r^2 \implies (x+4)^2+(y-2)^2 = 50\)

Answer 34

got it thanks

Answer 35

yw