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If P and Q are two points whose coordina...

If P and Q are two points whose coordinates are `(at^2, 2at)` and `(a/t^2,[-2a]/t)` respectively and S is the point (a, 0), show that `1/[SP]+1/[SQ]` is independent of t

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let points `P,Q,S `are
`Q = (a/t^2, (-2a)/t) `
`P = (at^2, 2at)`
`S= (a,0)`
`SP=sqrt ((a-at^2)^2+(0-2at)^2)`
`=sqrt (a^2+a^2t^4-2a^2t^2+4a^2t^2)`
`=sqrt (a^2+a^2t^4+2a^2t^2)`
`SP = sqrt ((a+at^2)^2)`
...
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