Question

If you transform x 2 + y 2 = 25 into 4x 2 + 4y 2 = 25, which option below describes the effect of this transformation on the radius?

a. It divides the radius by 4.
b. It multiplies the radius by 4.
c. It divides the radius by 2.
d. It multiplies the radius by 2.

Answer 1

c. It divides the radius by 2.

Step-by-step explanation

The general equation of a circle is

(x-h)² + (y-k)² = r²

Where (h, k) makes the coordinates of the circle and r the radius.

x² + y² = 25 For this equation,

center (0, 0)

Radius = √25 = 5

4x² + 4y² = 25 First simplify this equation

4x² + 4y² = 25 ⇒ x² + y² = 25/4

center (0, 0)

Radius = √(25/4) = 5/2

The radius has been divided by 2