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Question-186952

Question Number 186952 by Humble last updated on 12/Feb/23 Answered by horsebrand11 last updated on 12/Feb/23 $${let}\:\mathrm{3}{x}+\mathrm{2}{y}+{c}\:=\:\mathrm{0}\:{is}\:{tangent}\:{to} \\ $$$${hypebola}\:.\:{we}\:{have}\:\frac{\mathrm{1}}{\mathrm{12}}{x}−\frac{\mathrm{1}}{\mathrm{9}}{y}.{y}'=\mathrm{0} \\ $$$$\Rightarrow{y}'=\frac{\frac{\mathrm{3}}{\mathrm{36}}{x}}{\frac{\mathrm{4}}{\mathrm{36}}{y}}\:=\:\frac{\mathrm{3}{x}}{\mathrm{4}{y}}\:=\:−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\Rightarrow{x}=−\mathrm{2}{y}\:{and}\:\frac{\mathrm{4}{y}^{\mathrm{2}} }{\mathrm{24}}−\frac{{y}^{\mathrm{2}} }{\mathrm{18}}\:=\mathrm{1}…

a-square-s-one-diagonal-s-terminal-points-are-5-0-9-4-what-are-the-coordinate-of-other-diagonal-s-terminal-points-

Question Number 121393 by faysal last updated on 07/Nov/20 $${a}\:{square}'{s}\:{one}\:{diagonal}'{s}\:{terminal}\:{points}\:{are} \\ $$$$\left(\mathrm{5},\mathrm{0}\right),\:\left(\mathrm{9},\mathrm{4}\right)\:{what}\:{are}\:{the}\:{coordinate}\:{of} \\ $$$${other}\:{diagonal}'{s}\:{terminal}\:{points} \\ $$ Answered by TANMAY PANACEA last updated on 07/Nov/20 $${Disgonal}\:{eqn}\:\:\frac{{y}−\mathrm{0}}{\mathrm{0}−\mathrm{4}}=\frac{{x}−\mathrm{5}}{\mathrm{5}−\mathrm{9}}\rightarrow{x}−{y}−\mathrm{5}=\mathrm{0}…

Question-121380

Question Number 121380 by aurpeyz last updated on 07/Nov/20 Answered by TANMAY PANACEA last updated on 07/Nov/20 $$\underset{{x}\rightarrow\mathrm{0}.\mathrm{5}−\:\frac{}{}} {\mathrm{li}{m}} \\ $$$${li}\underset{{x}\rightarrow\mathrm{0}.\mathrm{5}−} {{m}}\:\sqrt{\frac{{x}+\mathrm{2}}{{x}+\mathrm{1}}}\:=\sqrt{\frac{\mathrm{2}.\mathrm{5}}{\mathrm{1}.\mathrm{5}}}\:=\sqrt{\frac{\mathrm{5}}{\mathrm{3}}}\: \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{think}}\:\boldsymbol{{so}} \\…