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:It's not my first way of thinking about these things, but perhaps this would be clearer if I did it with coordinates. Let V({{mvar|a}},0) be the vertex, F({{mvar|c}},0) a focus. The line from F that is perpendicular to the asymptote with equation {{math|1=''y'' = {{sfrac|''b''|''a''}}''x''}} has equation {{math|1=''y'' = −{{sfrac|''a''|''b''}}''x'' + {{sfrac|''ac''|''b''}}}}. So, the point of intersection P has coordinates {{math|({{sfrac|''a''<sup>2</sup>|''c''}}, {{sfrac|''ab''|''c''}})}}. Now the distance from P to F can be calculated to be {{mvar|b}} and the distance from P to O is calculated to be {{mvar|a}} (with heavy use of the relation {{math|1=''a''<sup>2</sup> + ''b''<sup>2</sup> = ''c''<sup>2</sup>}}.) --[[User:Wcherowi|Bill Cherowitzo ]] ([[User talk:Wcherowi#top|talk]]) 16:32, 14 March 2017 (UTC)
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