Question 70
Consider the system
$$
\begin{cases}
x^{2} + y^{2} = a^{2} + 2 \\
\dfrac{1}{x} + \dfrac{1}{y} = a
\end{cases}
$$
where $a$ is a real number.
a) Solve the system for $a=0$.
b) Find all $a$, for which the system has exactly two solutions.
$$
\begin{cases}
x^{2} + y^{2} = a^{2} + 2 \\
\dfrac{1}{x} + \dfrac{1}{y} = a
\end{cases}
$$
where $a$ is a real number.
a) Solve the system for $a=0$.
b) Find all $a$, for which the system has exactly two solutions.