MaTh HeLp PlEaSe!?

Question

Okay, so this is a circle equation:

xSquared+ySquared-5x+4y-13=0

I need to split it into two functions.

So, the question is: ... Begin by writing the circle as the union of two functions. Identify the functions that represent the top half and the bottom half of the circle.

Thanks. ♥BeautiifuLChick♥

Answer 1

Ok, now it may not look like it, but it is asking you to put it into the form y=.

so...
x^2+y^2 - 5x + 4y - 13 = 0
So, lets complete the square on both the x and y values.

x^2 - 5x + 2.5^2 +y^2 + 4y +2 = 2.5^2 + 4 (adding (1/2 * 5)^ and (a/2 * 4)^2 to each side. Simplifying it gives...
(x - 2.5)^2 + (y + 2)^2 =16.5
(y+2)^2 = 16.5 - (x-2.5)^2

When we square root both sides we get:
y+2 = (+/-) sqrt (16.5 - (x-2.5)^2)
y = -2 (+/-) sqrt (16.5 - (x-2.5)^2)

Because we have the (+/-), we have two seperate equations. The top of the circle is given by:
y= -2 + sqrt (16.5 - (x-2.5)^2)
And the bottom of the circle is:
y = -2 - sqrt (16.5 - (x-2.5)^2)

Answer 2

Don't think that is going to work. Better to try to form perfect squares with the function. For example, you have y^2+4y and you can "add" 4 as long as you subtract it.
Then x^2-5x+(y+2)^2=17
You can do the same with the x terms and you will wind up with a circle which is offset from the origin.
The sqrt of the number on the right hand side will be the radius of the circle.

Answer 3

x^2 + y^2 -5x +4y - 13 = 0
x^2 - 5x + y^2 + 4y = 13
(x - 5/2)^2 - 25/4 + (y+2)^2 + 4 = 13
(x - 5/2)^2 + (y+2)^2 = 61/4