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Question Number 9731 by tawakalitu last updated on 29/Dec/16

Find the asymptotes of the hypebola whose equation is given by. (x/(24)) − (y/(29)) = 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{asymptotes}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hypebola}\:\mathrm{whose} \\ $$$$\mathrm{equation}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}. \\ $$$$\frac{\mathrm{x}}{\mathrm{24}}\:−\:\frac{\mathrm{y}}{\mathrm{29}}\:=\:\mathrm{1} \\ $$

Commented by geovane10math last updated on 29/Dec/16

((29x − 24y)/(696)) = 1 29x − 24y = 696 29x − 696 = 24y y = ((29x − 696)/(24)) = ((29x)/(24)) − 29 y is a function f(x) = ax + b , a = ((29)/(24)) and b = −29

$$\frac{\mathrm{29}{x}\:−\:\mathrm{24}{y}}{\mathrm{696}}\:=\:\mathrm{1} \\ $$$$\mathrm{29}{x}\:−\:\mathrm{24}{y}\:=\:\mathrm{696} \\ $$$$\mathrm{29}{x}\:−\:\mathrm{696}\:=\:\mathrm{24}{y} \\ $$$${y}\:=\:\frac{\mathrm{29}{x}\:−\:\mathrm{696}}{\mathrm{24}}\:=\:\frac{\mathrm{29}{x}}{\mathrm{24}}\:−\:\mathrm{29} \\ $$$${y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ax}\:+\:\mathrm{b}\:,\:{a}\:=\:\frac{\mathrm{29}}{\mathrm{24}}\:\mathrm{and}\: \\ $$$${b}\:=\:−\mathrm{29} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Answered by sandy_suhendra last updated on 29/Dec/16

the equation of hyperbola ≡(((x−h)^2 )/a^2 )−(((y−k)^2 )/b^2 )=1 the centre of hyperbola =(h,k)=(0,0) a^2 =24 ⇒ a=2(√6) b^2 =29 ⇒ b=(√(29)) the equation of hyperbola asymtotes : y=±(b/a)(x−h)+k ⇒ y=±((√(29))/(2(√6))) x ⇒ y=±((√(174))/(12)) x

$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{hyperbola}\:\equiv\frac{\left(\mathrm{x}−\mathrm{h}\right)^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }−\frac{\left(\mathrm{y}−\mathrm{k}\right)^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{hyperbola}\:=\left(\mathrm{h},\mathrm{k}\right)=\left(\mathrm{0},\mathrm{0}\right) \\ $$$$\mathrm{a}^{\mathrm{2}} =\mathrm{24}\:\Rightarrow\:\mathrm{a}=\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\mathrm{b}^{\mathrm{2}} =\mathrm{29}\:\Rightarrow\:\mathrm{b}=\sqrt{\mathrm{29}} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{hyperbola}\:\mathrm{asymtotes}\::\:\mathrm{y}=\pm\frac{\mathrm{b}}{\mathrm{a}}\left(\mathrm{x}−\mathrm{h}\right)+\mathrm{k} \\ $$$$\Rightarrow\:\mathrm{y}=\pm\frac{\sqrt{\mathrm{29}}}{\mathrm{2}\sqrt{\mathrm{6}}}\:\mathrm{x} \\ $$$$\Rightarrow\:\mathrm{y}=\pm\frac{\sqrt{\mathrm{174}}}{\mathrm{12}}\:\mathrm{x} \\ $$

Commented by tawakalitu last updated on 29/Dec/16

i really appreciate sir. God bless you.

$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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