Question Number 25536 by tawa tawa last updated on 11/Dec/17
$$\mathrm{If}\:\:\:\mathrm{x}\:=\:\mathrm{2sec}\left(\mathrm{3t}\right)\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{4tan}\left(\mathrm{3t}\right),\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\mathrm{y}\:=\:\mathrm{4}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right) \\ $$
Answered by prakash jain last updated on 11/Dec/17
$${x}=\mathrm{2sec}\:\mathrm{3}{t}\Rightarrow\frac{{x}}{\mathrm{2}}=\mathrm{sec}\:\mathrm{3}{t} \\ $$$${y}=\mathrm{4tan}\:\mathrm{3}{t}\Rightarrow\frac{{y}}{\mathrm{4}}=\mathrm{tan}\:\mathrm{3}{t} \\ $$$$\mathrm{sec}^{\mathrm{2}} \theta−\mathrm{tan}^{\mathrm{2}} \theta=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{4}}−\frac{{y}^{\mathrm{2}} }{\mathrm{16}}=\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\mathrm{4}}=\frac{{y}^{\mathrm{2}} }{\mathrm{16}} \\ $$$$\Rightarrow{y}^{\mathrm{2}} =\mathrm{4}\left({x}^{\mathrm{2}} −\mathrm{4}\right) \\ $$
Commented by tawa tawa last updated on 13/Dec/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$