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(C) The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,which can be written as $\frac{1}{a}x + \frac{1}{b}y - 1 = 0$. The l

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$\frac{1}{p^2}$

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(C) The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,which can be written as $\frac{1}{a}x + \frac{1}{b}y - 1 = 0$. The length of the perpendicular $p$ from the origin $(0,0)$ to the line $Ax + By + C = 0$ is given by $p = \left| \frac{C}{\sqrt{A^2 + B^2}} \right|$. Substituting the values $A = \frac{1}{a}$,$B = \frac{1}{b}$,and $C = -1$,we get $p = \left| \frac{-1}{\sqrt{(\frac{1}{a})^2 + (\frac{1}{b})^2}} \right|$. Squaring both sides,we have $p^2 = \frac{1}{\frac{1}{a^2} + \frac{1}{b^2}}$. Therefore,$\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{p^2}$.

$p$ is the length of the perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$ respectively,then $\frac{1}{a^2} + \frac{1}{b^2}$ equals

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