Proving a function(with two variables) is continuous I am having a difficulty solving this problem. First of all, I'm sorry that the problem isn't well written but I am not very good with typing out math problems, due to the fact that I am new to this, so I hope it's at least understandable. Next, I want to say that I've tried solving this using polar coordinates and also by changing y with  $y=kx$, $y=kx^2$. But it didn't work. Anyway, the problem says: Find parameter a so that a function is continuous. (I tried to translate it correctly in English.) I hope someone can help me solve this problem, I would be so grateful.
$$
f(x,y) =
 \begin{cases} 
      \dfrac{5 - \sqrt{25-x^2-y^2}}{7 - \sqrt{49-x^2-y^2}} & (x,y)\neq (0,0) \\
        \\
      a & (x,y)=(0,0) 
   \end{cases}
$$

Hint:
You only need to determine, in polar coordinates,  $\;\displaystyle\lim_{r\to 0}\,\dfrac{5 - \sqrt{25-x^2-y^2}}{7 - \sqrt{49-x^2-y^2}}$.
Rewrite this fraction, with the conjugate expressions, as
$$\frac{5 - \sqrt{25-r^2}}{7 - \sqrt{49-r^2}}=\frac{5^2 - (25-r^2)}{5 + \sqrt{25-r^2}}\, \frac{7 +\sqrt{49-r^2}}{7^2 -(49-r^2)}.$$
Can you end the calculations?
