Hello, Tangera!

A little thought will give you the answer . . .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:

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?

What does it mean when a point inona graph?

. . It means that the coordinates of the pointsatisfythe equation.

Given the circle:

Where is the origin (0,0) relative to the circle?

. . Substitute

(0,0) satisfies the equation . . . The origin isonthe circle.

Where is (1,3) ?

. . Substitute

(1,3) isinsidethe circle.

Where is (3,5) ?

. . Substitute

(3,5) isoutisdethe circle.

The same procedure applies to ellipses.