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

1 Answer
Jul 8, 2015

Answer:

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]}