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Question Number 87952 by ajfour last updated on 07/Apr/20

Commented by ajfour last updated on 07/Apr/20

$$whatisc?Sir.$$

Commented by ajfour last updated on 07/Apr/20

$$FindequationoflineABCDin$$$$termsofellipseparameters$$$$aandb.$$

Commented by Prithwish Sen 1 last updated on 07/Apr/20

$$\mathrm{I}\mathrm{got}$$$$\mathbf{y}-\mathbf{c}=\frac{\mathbf{b}}{\mathbf{a}}.\sqrt{\frac{{\mathbf{b}}^2-{\mathbf{c}}^2}{9{\mathbf{c}}^2-{\mathbf{b}}^2}}.\mathbf{x}$$$$\mathbf{please}\mathbf{check}$$

Commented by john santu last updated on 07/Apr/20

$$\mathrm{c}=\sqrt{{\mathrm{a}}^2-{\mathrm{b}}^2}$$

Commented by Prithwish Sen 1 last updated on 07/Apr/20

$$\mathrm{D}(\mathrm{acos}\theta ,\mathrm{bsin}\theta )\mathrm{A}(\mathrm{acos}\alpha ,-\mathrm{bsin}\alpha )$$$$\mathrm{Considering}\mathrm{C}$$$$2\sin \theta -\sin \alpha =0...\mathrm{i}$$$$\mathrm{and}\mathrm{considering}\mathrm{B}\cos \theta +2\cos \alpha =0...\mathrm{ii}$$$$\mathrm{the}\mathrm{equation}\mathrm{is}$$$$\mathrm{y}-\mathrm{bsin}\theta =\frac{\mathrm{b}(\sin \theta +\sin \alpha )}{\mathrm{a}(\cos \theta -\cos \alpha )}(\mathrm{x}-\mathrm{axcos}\theta )...\mathrm{iii}$$$$\mathrm{solving}\mathrm{the}\mathrm{three}\mathrm{equations}$$$$\frac{\mathbf{x}}{2\mathbf{a}}-\frac{\mathbf{y}}{\mathbf{b}}=\frac{1}{\sqrt{5}}$$$$\mathbf{sir}\mathbf{please}\mathbf{check}.$$$$$$$$$$

Answered by ajfour last updated on 07/Apr/20

$$Let\underset{-}{eq.ofline}be$$$$\frac{x}{p}-\frac{y}{q}=1,slopem=\frac{q}{p}$$$$l=\sqrt{p^2+q^2}$$$$D\equiv (2p,q);A\equiv (-p,-2q)$$$$\frac{4p^2}{a^2}+\frac{q^2}{b^2}=1\mathrm{\&}\frac{p^2}{a^2}+\frac{4q^2}{b^2}=1$$$$\Rightarrow \frac{15p^2}{a^2}=3\Rightarrow p=\frac{a}{\sqrt{5}}$$$$\mathrm{\&}\frac{15q^2}{b^2}=3\Rightarrow q=\frac{b}{\sqrt{5}}$$$$\Rightarrow eq.oflineis$$$$\frac{x}{a}-\frac{y}{b}=\frac{1}{\sqrt{5}}.$$

Commented by ajfour last updated on 07/Apr/20

$$SenSir,pleasecheckmy{sol}^n.$$

Commented by Prithwish Sen 1 last updated on 07/Apr/20

$$\mathrm{sir}\mathrm{yours}\mathrm{is}\mathrm{right}\mathrm{but}\mathrm{please}\mathrm{check}\mathrm{mine}.\mathrm{I}\mathrm{cannot}$$$$\mathrm{find}\mathrm{any}\mathrm{wrong}\mathrm{in}\mathrm{my}\mathrm{calculation}.\mathrm{please}\mathrm{help}$$

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