Equation of a half circle

• Jun 7th 2010, 11:58 AM
tigergirl
Equation of a half circle
Find an expression for the for the function whose graph is the given curve. Give the domain and range.

The bottom half of the circle whose center is @(3,0) and has a radius of length 5.

I'm so lost.
• Jun 7th 2010, 12:29 PM
p0oint
Here is the equation of the whole circle.

$\displaystyle (x-3)^2+y^2=5^2$

Now find y1 and y2, the negative square root would be the botom half of the circle.

Regards.
• Jun 7th 2010, 12:32 PM
SpringFan25
Lets find the equation of the full circle first.

This is $\displaystyle y^2 + (x-3)^2 = 5^2$

Rearrange for Y

This is $\displaystyle y = \sqrt{25 - (x-3)^2}$

When it is in this form, the range and domain are defined as follows:
The domain is all possible values that x can take
The range is all possible values that y can take

Because it is a circle with radius 5, centered around (3,0); you know the domain and range are:
Domain: $\displaystyle -2 \leq x \leq 8$
Range: $\displaystyle -5 \leq y \leq 5$

You want the bottom half of the circle, which is the part where Y<0.
Hopefully, you can see that
Domain: $\displaystyle -2 \leq x \leq 8$ (the same)
Range: $\displaystyle -5 \leq y \leq 0$ (bottom half only)

This is much easier to draw than do in your head. I'll try to attach an image later

edit too slow
• Jun 8th 2010, 06:33 PM
Altermeris
I got the same answer as SpringFan25. (Nod)