Question

graph the system of inequalities: (
x-3)^2/9 + (y+2)^2/4<=1
and (x-3)^2+(y+2)^2>=4

I do not know how to simplify this down enough to graph it

Answer 1

The first appears to be a all within a circle of radius 1, centered at (3,-2). Is that correct?

The second is a outside a circle of radius 2, centered at 3,-2

You do not need to simplify it, you need to RECOGNIZE a conic equation when you see one. Circle, parabola, hyperbola, and ellipse equations you should recognize those on sight. If you do not, get the standard forms on flashcards (they work) and MEMORIZE them.

Answer 2

I thought the first was an ellipse and the second was a circle

Answer 3

Go on: wolframalpha dot com

When page be open in rectangle type:

( x-3)^2/9 + (y+2)^2/4<=1 , (x-3)^2+(y+2)^2>=4

and click option =


After few seconds you will see everything about your inequalities,including graph.

Answer 4

Thank you both so much.