Fourier transform involving a dirac delta function

Question

I know that $\int \delta(x-a)f(x) dx =f(a) $ , the fundamental defining property of the delta function. How does this change if we no longer consider $x-a$ but $a^2 -x^2$, such that the integral is now $\int_{-\infty}^{\infty} \delta(a^2 -x^2)f(x) dx$? Thank you for any help in advance

Answer 1

you can look on this formula

now you can apply sum formula and you should get

$f(a)/(|2*a|)+f(-a)/|2*a|$

also imagine that $(a-x)=-(x-a)$