Question

How do you graph `(x-4)^2 + (y-5)^2 < 9`?

Answer 1

Pretend that the inequality is an equality, solve the equation and plot the graph. Shade all areas that satisfy the inequality.

Explanation:

`(x-4)^2 + (y-5)^2 < 9`

This is the standard form for the equation of a circle with centre at (`4,5`) and radius `sqrt9 = 3`.

This means that, from the centre, you go 3 units to the right, 3 to the left, 3 up, and 3 down.

Thus, the four extreme points are at (`4,8`), (`4,2`) (`1,5`), and (`7,5`).

Since the inequality is "< 9", you use a dotted line for the graph, and you shade all areas for which `y<9`.

graph{(x-4)^2 + (y-5)^2 < 9 [-6.41, 13.59, -1.04, 8.96]}