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  • If the length of the perpendicular drawn from origin to the line whose intercepts on the axes are a and b be p, then <spa

If the length of the perpendicular drawn from origin to the line whose intercepts on the axes are a and b be p, then 

Option: 1

a^2+b^2=p^2


Option: 2

a^2+b^2=\frac{1}{p^2}


Option: 3

\frac{1}{a^2}+\frac{1}{b^2}=\frac{2}{p^2}


Option: 4

\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}


Answers (1)

best_answer

Equation of line is  \frac{x}{a}+\frac{y}{b}=1 \quad \Rightarrow b x+a y-a b=0

Perpendicular distance from origin to given line is

p=\left|\frac{-a b}{\sqrt{a^2+b^2}}\right| \Rightarrow \frac{\sqrt{a^2+b^2}}{a b}=\frac{1}{p} \Rightarrow\frac{a^2+b^2}{a^2 b^2}=\frac{1}{p^2} \Rightarrow \frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}

Posted by

vishal kumar

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