In a right triangle with sides $x$ and $y$ and hypotenuse $z$, the altitude drawn on the hypotenuse is $a$, then,

Question

$\begin{array}{1 1} (a)\; xy=a^2 \\ (b)\; \frac{1}{x} + \frac{1}{y}= \frac{1}{a} \\ (c)\; x^2+y^2=2a \\ (d)\; \frac{1}{x^2} + \frac{1}{y^2} = \frac{1}{a^2} \end{array}$