To expand horizontally with scale factor 2, change "x" to "x/2" in equation.

To compress horizontally with scale factor 2, think of it as expanding with scale factor 1/2, so change "x" to "x/(1/2)" -- which is same as replacing "x" with "2x".

So in first example, you are compressing with scale factor 2, so replace "x" with "2x"

(2x)^2 / 4 - (y - 3)^2 / 36 = 1

This simplifies to 4x^2 / 4, or x^2 as you wrote.

x^2 - (y - 3)^2 / 36 = 1

On graph, every point is transformed horizontally so its horizontal distance from the y-axis is 1/2 what it was originally.

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To expand vertically with scale factor 2, change "y" to "y/2" in equation.

To compress vertically with scale factor 2, think of it as expanding with scale factor 1/2, so change "y" with "y/(1/2)" -- which is same as replacing "y" with "2y."

In second example, you are expanding vertically with scale factor 2, so replace y with y/2

(x + 2)^2 + ((y/2) - 3)^2 = 25

Now simplify.

(x + 2)^2 + ((y - 6)/2)^2 = 25

(x + 2)^2 + (y - 6)^2 / 4 = 25

Divide both sides by 25.

(x + 2)^2 / 25 + (y - 6)^2 / 100 = 1