Question

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

Answer 1

Answer:

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

Step-by-step 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:

$4x^2+4y^2=25\\x^2+y^2=\frac{25}{4} \\x^2+y^2=(\frac{5}{2})^2$

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