Graph transformations

**Tangera** · March 19th 2008, 04:48 AM

Hello!

I am unsure about how to determine if the origin is located inside, outside or on the circle or ellipse after a graph transformation. For example, given the equation of the circle to be (x+3)^2 + (y-4)^2 = 5 , how do I know if the origin is within or outside or a point on the graph itself? How about in the case of an ellipse?

Thank you!

**Soroban** · March 19th 2008, 07:38 AM

Hello, Tangera!

I am unsure about how to determine if the origin is located inside,
outside or on the circle or ellipse after a graph transformation.

For example, given the equation of a circle: $(x+3)^2 + (y-4)^2 \:= \:5^2$
how do I know if the origin is within or outside or a point on the graph itself?
How about in the case of an ellipse?

A little thought will give you the answer . . .

What does it mean when a point in on a graph?
. . It means that the coordinates of the point satisfy the equation.

Given the circle: $(x+3)^2 + (y-4)^2\:=\:5^2$

Where is the origin (0,0) relative to the circle?
. . Substitute $x=0,\:y=0\!:\;\;(0+3)^2 + (0-4)^2 \;=\;3^2 + (-4)^2 \;\;{\bf{\color{blue}= \;25}}$
(0,0) satisfies the equation . . . The origin is on the circle.

Where is (1,3) ?
. . Substitute $x=1,y=3\!:\;\;(1+3)^2 + (3-4)^2 \:=\:16 + 1 \:=\:17 \;\;{\bf{\color{blue}<\:25}}$
(1,3) is inside the circle.

Where is (3,5) ?
. . Substitute $x=3, y=5\!:\;\;(3+3)^2 + (5-4)^2 \:=\:37\;\;{\bf{\color{blue}> \;25}}$
(3,5) is outisde the circle.

The same procedure applies to ellipses.

**Tangera** · March 20th 2008, 01:22 AM

I get it! I get it!! Thank you very very much!!

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