Question Number 199392 by Calculusboy last updated on 03/Nov/23
Answered by mr W last updated on 03/Nov/23
$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{53} \\ $$$$\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{13} \\ $$$$ \\ $$$${eqn}.\:{of}\:{intersection}\:{line}: \\ $$$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} −\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\left({y}+\mathrm{4}\right)^{\mathrm{2}} −\left({y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{53}−\mathrm{13} \\ $$$$−\mathrm{5}\left(\mathrm{2}{x}−\mathrm{1}\right)+\mathrm{5}\left(\mathrm{2}{y}+\mathrm{3}\right)=\mathrm{40} \\ $$$$−{x}+{y}=\mathrm{2} \\ $$$$\Rightarrow{y}={x}+\mathrm{2} \\ $$$$ \\ $$$${intersection}\:{points}: \\ $$$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({x}+\mathrm{2}+\mathrm{4}\right)^{\mathrm{2}} =\mathrm{53} \\ $$$${x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{4}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}+\mathrm{4}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}_{\mathrm{1}} =−\mathrm{4},\:{x}_{\mathrm{2}} =\mathrm{1} \\ $$$$\Rightarrow{y}_{\mathrm{1}} =−\mathrm{2},\:{y}_{\mathrm{2}} =\mathrm{3} \\ $$$${i}.{e}.\:{intersection}\:{at}\:\left(−\mathrm{4},−\mathrm{2}\right)\:{and}\:\left(\mathrm{1},\mathrm{3}\right) \\ $$
Commented by Calculusboy last updated on 03/Nov/23
$$\boldsymbol{{thanks}}\:\boldsymbol{{sir}} \\ $$