How do you graph (x+3)^2 + (y-2)^2 = 25?

1 Answer
Apr 10, 2016

x intercepts at: x=+-sqrt21-3
y intercepts at: y= +-4+2
Centre Point at: (-3,2)
Radius of: 5

Explanation:

The function is a circular function:

The general form of a circular function can be expressed as:

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

Where the centre point of the graph is present at the point (h,k)
and the solution (the number after the = sign) is the radius of the circle squared.

Therefore, from your function:

(x+3)^2+(y-2)^2=25

We can determine that:

The centre point of the function is present at the point (-3,2) and the radius is sqrt25=5

For any function, x incepts where y = 0

Therefore, by substituting y=0 we get:

(x+3)^2+(-2)^2=25

By simplifying this and solving for x we get:

(x+3)^2+4=25
(x+3)^2=25-4
(x+3)^2=21
(x+3)=+-sqrt21
Remember that any real square has two solutions (a positive and negative), hence the +-sqrt21
x=+-sqrt21-3
Therefore, two x intercepts are present:
One at: x=-sqrt21-3
The other at: x=+sqrt21-3

For any function, y intercepts where x = 0

Therefore, if we substitute x = 0 into your equation, we get:

(0+3)^2+(y-2)^2=25

By simplifying and solving for y we get:

9+(y-2)^2=25
(y-2)^2=16
Again, remember that any real square has two solutions (a positive and negative), hence the +-sqrt16
(y-2)=+-sqrt16
(y-2)=+-4
y=+-4+2
Therefore, two y intercepts are present:
One at: y=-2 calculated as: [-4+2]
The other at: y=6 calculated as: [+4+2]

To summarise:

If we plot all of our points on the graph, we get:

Centre Point at: (-3,2)

Radius of: 5

x Intercepts at: x= +sqrt21-3 and x=-sqrt21-3

y Intercepts at: y=-2 and y=6
graph{(x+3)^2+(y-2)^2=25 [-21.42, 18.58, -7.32, 12.68]}