If P and Q are two points whose coordinates are `(a t^2,2a t)a n d(a/(t^2),(2a)/t)` respectively and S is the point (a,0). Show that `1/(S P)+1/(s Q)` is independent of t.

Explanation

`SP=sqrt[(at^2-a)^2+(2at-0)^2]=asqrt[(t^2-1)^2+4t^2]=a(t^2+1)`


And `SQ=sqrt[(a/t^2-a)^2-((2a)/t-0)^2]`


`=> SQ=sqrt[(a^2(1-t^2)^2)/t^4+(4a^2)/t^2]`


`=> SQ=a/t^2 sqrt[(1-t^2)^2+4t^2]`


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