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(D) The equation of the line with intercepts $a$ and $b$ on the axes is given by $\frac{x}{a} + \frac{y}{b} = 1$,which can be rewritten as $bx + ay -

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

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(D) The equation of the line with intercepts $a$ and $b$ on the axes is given by $\frac{x}{a} + \frac{y}{b} = 1$,which can be rewritten as $bx + ay - ab = 0$.The length of the perpendicular $p$ from the origin $(0, 0)$ to this line is given by the formula $p = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$.Substituting the values,we get $p = \frac{|b(0) + a(0) - ab|}{\sqrt{b^2 + a^2}} = \frac{|-ab|}{\sqrt{a^2 + b^2}}$.Squaring both sides,we have $p^2 = \frac{a^2 b^2}{a^2 + b^2}$.Taking the reciprocal,we get $\frac{1}{p^2} = \frac{a^2 + b^2}{a^2 b^2} = \frac{a^2}{a^2 b^2} + \frac{b^2}{a^2 b^2} = \frac{1}{b^2} + \frac{1}{a^2}$.Thus,$\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{p^2}$.

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

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