Serious math 12 help!?

Question

Hey guys,
I am in Math 12 and I need some help with my review on transformations. Please help if you can.

If the graph x^2 + y^2 = 4 is vertically compressed by a factor of 1/5, then reflected in the y-axis, determine an equation for the graph.

Answer 1

To compress it vertically by a factor of 5, replace y with 5y

x^2 + (5y)^2 = 4

Now reflect it on the y-axis by replacing y by (-y)

x^2 + (-5y)^2 = 4
x^2 + 25y^2 = 4

If you actually meant compressing the graph by a factor of 1/5 (dilating the graph by a factor of 5), you would get:

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

Answer 2

First and foremost, it is best to realize what the graph of the original equation looks like.

x^2 + y^2 = r^2 is the basic equation for a circle. In your case, the circle has its center at the origin and has a radius of 2.

So, since it's a circle, the reflection about the y-axis will do nothing to the graph. The object is symmetric about that axis before and after the compression.

The compression means that the graph is now an ellipse with a major axis radius of 2 and a minor axis radius of 2/5.

Remember that the equation for an ellipse with a major axis in the x direction is:

x^2 / a^2 + y^2 / b^2 = 1 Where a and b are the radii of the axis.

So, you are left with: x^2 / 4 + 25 /4 * y^2 = 1 or, in a nicer, no fractions way:

x^2 + 25 y^2 = 4

Answer 3

X^2 + (Y)^2 = 4 . . . this is a circle of radius 2
X^2/4 + (Y)^2/4 = 1 . . . this also a circle in the form of ellipse
X ^2 /4 + Y ^2 / (2/5)^2 = 1
X ^2/4 + 25 Y ^2 / 4 = 1 . . . equation when y is compressed by
1/5