Graphing circles, help please?

Question

I know I can graph circles using the standard equation when the circle equation is simple like x²+y²=1,where the center is at (0,0), and I put √(1-x²) and -√(1-x²) into the calculator,

but once the equation gets complicated with the center somewhere else besides the origin, I don't know how to write it into the equation.

For example: (x-2)²+(y+1)²=1, I know how to graph manually with center at (2,1), but how do I graph this on a scientific calculator?

I know I have to get "y" by itself by subtracting (x-2)², but do I take the square root then subtract the one or vice versa?

I know this is a bit long, but any help is appreciated. Thanks.

Answer 1

Hi,

I am talking from TI83 experience. When I'd want to graph (x-2)²+(y+1)²=1, solve it for y. First. move (x-2)² to the other side:

(y+1)²=1-(x-2)²

Now you want to eliminate the square on the left side so you can solve for y. To do this, take the square root on both sides, remembering that there will be a ± in front of the right side.

(y+1)²=1-(x-2)²
.._____........_______
√(y+1)² = ±√(1-(x-2)²)

The square and square root on the left side cancel each other leaving:

................_______
y+1 = ±√(1-(x-2)²)

Now subtract the 1.

..............._______
y = -1 ±√(1-(x-2)²)


You need to type this in as 2 equations since calculator don't allow ±. Enter

.................._______
Y1 = -1 + √(1-(x-2)²) This graphs the top half of the circle.

.................._______
Y2 = -1 - √(1-(x-2)²) This graphs the bottom half of the circle.


A second way you could do it is to make

.........._______
Y1 = √(1-(x-2)²)

Then make

Y2 = -1 + Y1
Y3 = -1 - Y1

If you do it this way, be sure to turn off Y1 so it doesn't graph separately. Y1 comes from under VARS, Function. Remember your circle won't look like a circle on the normal screen unless you go to Zoom, 5 ZSquare to get the window drawn with appropriate scales on your rectangular window.

I hope this helps!! :-)

Answer 2

Ok so this is how I see it... A bar graph is best used when you are making a few comparisons with specific numerical values. However, a bar graph becomes a bit cumbersome if you have too many values or are making too many comparisons. Ex. Max Height of a peach tree vs Max Height of Apple tree, etc. A line graph is best used when comparing a lot of data points. Line graphs are wonderful in showing changes over time. Ex. Changes in height of a peach tree from 2000 to 2009 A pie graph ( circle graph) is the easiest in that each slice represents a piece of the whole. So if your messing with a percentage than Pie Graph is best. Ex. A portion of a total amount of peaches given to various individuals. Hope this helps a little. You get the feel for it the more you work with the various graphs.

Answer 3

If all you need is y = something then:

1. Put the y term by itself so subtract (x-2)² from both sides:
(y+1)²=1 - (x-2)²

2. Now take the square root to get y + 1:
y + 1 = SQRT(1 - (x - 2)^2)

3. Subtract off the 1 and get:
y = SQRT(1 - (x - 2)^2) - 1

Answer 4

the general equation for getting the equation of a circle is:

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

where:

h is the coordinate of the vertex (h,k)
k is the abscissa of the vertex (h,k)
r is the radius of the circle

Answer 5

Center at (a,b)

(x - a)^2 + (y - b)^2 = 1
so
(y - b)^2 = 1 - (x - a)^2
= 1 - (x^2 - 2ax + a^2)
= 1-a^2 + 2ax - x^2
y-b = + or - sqrt (1-a^2 + 2ax - x^2)
y = b + sqrt (1-a^2 + 2ax - x^2) or b - sqrt (1-a^2 + 2ax - x^2)