Question

Question and answer choices attached.

Answer 1

@KingGeorge can you help?

Answer 2

http://en.wikipedia.org/wiki/Circle
In an x–y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that
\[(x-a)^{2}+(y-b)^{2} = r^{2}\]
This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram to the right, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x − a and y − b. If the circle is centred at the origin (0, 0), then the equation simplifies to
\[x^{2}+y^{2} = r^{2}\]

Answer 3

Let's do this one step at a time. What do you think the center of the circle is?

Answer 4

i have no clue. ive never seen a circle as an equation before

Answer 5

As wired posted, if you have an equation for a circle that looks like \[(x-a)^2+(y-b)^2=r^2\]the center is at \((a, b)\) with radius \(r\).

Answer 6

the general form a a circle is

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

(h, k) is the centre and r is the radius.

in your equation what values do h and k have..?

Answer 7

You have \((x-1/2)^2+(y+1)^2=25/4\). So \(a=\)...?

Answer 8

a = -1/2

Answer 9

\[r^2 = \sqrt{\frac{25}{4}} = \frac{\sqrt{25}}{\sqrt{4}}\]

just evaluate for r

Answer 10

Careful, it should be \(+1/2\) since the general form is \((x-a)\).

Answer 11

oh alright^

Answer 12

a = 1/2 and b = -1

Answer 13

Perfect. Now look at what campbell wrote. Can you tell me what \(r\) is?

Answer 14

yeah i got the radius part i just didnt understand the center part. but now i do! Thanks @KingGeorge and @campbell_st !!!!! :)

Answer 15

so the answer is the 3rd choice

Answer 16

Guess I'm chopped liver lol :)

Answer 17

Bingo

Answer 18

sorry @Wired thanks for your help too! :D

Answer 19

lol no problem :)