For any two nonzero real numbers a and b if this line x a + y b = 1 is a tangent to the circle x 2 + y 2 = 1…

Given,

Equation of circle as $x^2+y^2=1$,

Now assuming a point $\left(x_1,y_1\right)$ on circle we have equation of tangent at this point given by $x{x}_1+y{y}_1=1 ...............\left(1\right)$,

Now given $\frac{x}{a}+\frac{y}{b}=1$ is tangent to the given circle so on comparing with equation $\left(1\right)$ we get, $x_1=\frac{1}{a} \& y_1=\frac{1}{b}$

So point lie on the circle.