How to enlarge a circle?

Question

if you are given a circle with equation $(x-a)^2 + (y-b^2) = r^2$ and it is enlarged by a factor of $3$ what would the new equation be?

Would you put $2x$ an $2y$ in the place of $y$?

Answer 1

To scale through a center by factor $\lambda$ use:

$$(x-a)^2 + (y-b)^2 = (\lambda r)^2$$

and to scale through the origin use:

$$\left(\frac{x}{\lambda}-a\right)^2 + \left(\frac{y}{\lambda}-b\right)^2 = r^2.$$

Blue is the original, violet was scaled through the origin and green through the center.

Picture courtesy by Wolfram Alpha.

I hope this helps $\ddot\smile$