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  • If the length of the perpendicular drawn from origin to the line whose intercept on the axes are a and b be p ,then prove that 1/a^2 +1/b^2=1/p^2

If the length of the perpendicular drawn from origin to the line whose intercept on the axes are a and b be p ,then prove that 1/a^2 +1/b^2=1/p^2

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Solution: The equation of the line is ,

x/a+y/b=1Rightarrow bx+ay-ab=0

Perpendicular distance from the origin to the given line is

p=left | -ab/sqrta^2+b^2 ight |Rightarrow sqrta^2+b^2/ab=1/p\ \Rightarrow a^2+b^2/a^2 imes b^2=1/p^2Rightarrow 1/a^2+1/b^2=1/p^2

Posted by

Deependra Verma

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