A circle passes through the focus S of conic and meets it in four points whose distance from S are `r_1,r_2, r_3, and r_4` prove that `1/(r_1)+1/(r_2)+1/(r_3) +1/(r_4) =2/l` where 2l is the latus rectum of the conic

Explanation

`l/r = (1 +e cos theta)`

`r = d cos ( theta - r)`

`r = d[ cos theta cos r +vsin theta sin r ]`

`cos theta = (l-r)/(er)`

`sin theta = sqrt(1 - ((l-r)/(er))^2)`

`r = d[((l-r)/(er)) cos r + sqrt(1 - ((l-r)/(er))^2 sin r)`

`[ er^2 - d(l-r) cos r ]^2 = d^2[e^2 r^2 - ((l-r)^2) sin^2 r]`

`e^2 r^4 + 2de (cos r )r^3 + (a^2 - 2eld cos r - e^2d^2 sin^2 r)r^2 - 2ld^2 r + d^2 l^2 = 0 `

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