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Question Number 139388 by mnjuly1970 last updated on 26/Apr/21

Answered by mr W last updated on 26/Apr/21

Commented by mr W last updated on 26/Apr/21

((b/2)/y)=cos α  ⇒(b^2 /y^2 )=4 cos^2  α  ((c/2)/x)=sin α  ⇒(c^2 /x^2 )=4 sin^2  α  (b^2 /y^2 )+(c^2 /x^2 )=4(cos^2  α+sin^2  α)=4

$$\frac{{b}/\mathrm{2}}{{y}}=\mathrm{cos}\:\alpha \\ $$$$\Rightarrow\frac{{b}^{\mathrm{2}} }{{y}^{\mathrm{2}} }=\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:\alpha \\ $$$$\frac{{c}/\mathrm{2}}{{x}}=\mathrm{sin}\:\alpha \\ $$$$\Rightarrow\frac{{c}^{\mathrm{2}} }{{x}^{\mathrm{2}} }=\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\alpha \\ $$$$\frac{{b}^{\mathrm{2}} }{{y}^{\mathrm{2}} }+\frac{{c}^{\mathrm{2}} }{{x}^{\mathrm{2}} }=\mathrm{4}\left(\mathrm{cos}^{\mathrm{2}} \:\alpha+\mathrm{sin}^{\mathrm{2}} \:\alpha\right)=\mathrm{4} \\ $$

Commented by mnjuly1970 last updated on 27/Apr/21

 thanks alot sir ....

$$\:{thanks}\:{alot}\:{sir}\:.... \\ $$

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