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Normal to a rectangular hyperbola at P m...

Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of `(SN)/(SP).`

Text Solution

Verified by Experts

We know that PN is angle bisector of focal radii SP and S'P.
`therefore" "(SP)/(S'P)=(SN)/(S'N)`
`therefore" "(SN)/(SP)=(S'N)/(S'P)=|(SN-S'N)/(SP-S'P)|=(SS')/(|SP-S'P|)=e=sqrt2`
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