Question Number 23104 by lizan 123 last updated on 26/Oct/17
$${show}\:{tht}\:{the}\:{curve}\:{with}\:{parametric}\:{equcations} \\ $$$${x}={t}^{\mathrm{2}} \:,{y}={t}^{\mathrm{3}} \:−\mathrm{9}{t}\:{intersect}\:{at}\:{the}\:{point}\:\left(\mathrm{9},\mathrm{0}\right). \\ $$
Answered by ajfour last updated on 26/Oct/17
$${y}={t}\left({t}^{\mathrm{2}} −\mathrm{9}\right)\: \\ $$$$\Rightarrow\:\:{y}^{\mathrm{2}} ={x}\left({x}−\mathrm{9}\right)^{\mathrm{2}} \\ $$$${double}\:{root}\:{at}\:{x}=\mathrm{9}\:,\:{so} \\ $$$${curve}\:{intersects}\:{itself}\:{at}\:{x}=\mathrm{9}\:. \\ $$