Prove that the product of the lengths of the perpendiculars drawn from the points `(sqrt(a^(2)-b^(2)), 0) " and" (-sqrt(a^(2)-b^(2)), 0) " to the line " (x)/(a) "cos " theta + (y)/(b) " sin" theta = 1 " is " b^(2).`

Explanation

Given,


`(axcostheta) /a+(y sin theta)/b =1`


Perpendicular distance from `(sqrt (a^2 -b^2), 0) = |[(a^2-b^2costheta /a) -1] / (sqrt ((costheta/a)^2 +(sintheta/b)^2))|`


Perpendicular distance from `(-sqrt (a^2 -b^2), 0)= |[(a^2-b^2costheta /a) -1] / (sqrt ((costheta/a)^2 +(sintheta/b)^2))|`


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