Question

If you transform x2+ y2 = 25 into 4x2+ 4y2 = 25, which option below describes the effect of this transformation on the

radius?
It multiplies the radius by 2
It multiplies the radius by 4
It divides the radius by 4
It divides the radius by 2

Answer 1

It divides the radius by 2, which is the last option in your list of possible answers.

Explanation:

Recall that the standard equation of a circle of radius R centered at the origin of coordinates is given by:

`x^2+y^2=R^2`

so when you have the first equation of the circle:

`x^2+y^2=R^2\\x^2+y^2=25\\x^2+y^2=5^2`

The radius of the circle was 5

Now, when you work with the second equation, we need to divide both sides by 4 in order to get the standard form of the circle and be able to understand what the radius is:

`4x^2+4y^2=25\\x^2+y^2=(25)/(4) \\x^2+y^2=((5)/(2))^2`

So we see that the initial radius 5 is now divided by 2.