Question Number 91933 by liki last updated on 03/May/20
Commented by liki last updated on 03/May/20
$$...\mathrm{please}\:\mathrm{mr}\:\mathrm{w}\:\mathrm{help}\:\mathrm{me}\:,\mathrm{emergency}!< \\ $$
Commented by liki last updated on 03/May/20
$$\mathrm{Qn}\:\mathrm{11} \\ $$
Answered by mr W last updated on 03/May/20
Commented by mr W last updated on 03/May/20
$${say}\:{the}\:{line}\:{parallel}\:{to}\:{y}−{axis}\:{is} \\ $$$${x}={u} \\ $$$${intersection}\:{with}\:{y}={x}^{\mathrm{2}} \:{at}\:{P}: \\ $$$${x}_{{P}} ={u},\:{y}_{{P}} ={u}^{\mathrm{2}} \\ $$$${intersection}\:{with}\:{y}={x}+\mathrm{2}\:{at}\:{Q}: \\ $$$${x}_{{Q}} ={u},\:{y}_{{Q}} ={u}+\mathrm{2} \\ $$$${mid}−{point}\:{of}\:{PQ}\:{is}\:{M}: \\ $$$${x}_{{M}} ={u},\:{y}_{{M}} =\frac{{y}_{{P}} +{y}_{{Q}} }{\mathrm{2}}=\frac{{u}^{\mathrm{2}} +{u}+\mathrm{2}}{\mathrm{2}}=\frac{{x}_{{M}} ^{\mathrm{2}} +{x}_{{M}} +\mathrm{2}}{\mathrm{2}} \\ $$$${i}.{e}.\:{the}\:{locus}\:{of}\:{point}\:{M}\:{is} \\ $$$${y}=\frac{{x}^{\mathrm{2}} +{x}+\mathrm{2}}{\mathrm{2}} \\ $$$${which}\:{is}\:{also}\:{a}\:{parabola}. \\ $$
Commented by liki last updated on 04/May/20
$$...\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:,\:\mathrm{be}\:\mathrm{blessed}\:! \\ $$