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Question Number 67852 by mr W last updated on 01/Sep/19

Commented by Prithwish sen last updated on 01/Sep/19

$$$$$$\mathbf{A}=(0,\mathbf{a}),\mathbf{B}=(\frac{-4}{\mathbf{a}},0),\mathbf{C}=(\frac{20}{\mathbf{a}},-9\mathbf{a}),\mathbf{D}=(\frac{2}{\mathbf{a}},0)$$$$\mathbf{E}=(0,\frac{-3\mathbf{a}}{2})$$$$\mathrm{Equation}\mathrm{of}\mathrm{line}\mathrm{passing}\mathrm{through}\mathrm{A}\mathrm{and}\mathrm{D}$$$$\mathbf{AC}\Rightarrow {\mathrm{a}}^2\mathrm{x}+2\mathrm{y}-2\mathrm{a}=0....\left(\mathrm{i}\right)$$$$\mathrm{Equation}\mathrm{of}\mathrm{line}\mathrm{passing}\mathrm{through}\mathrm{B}\mathrm{and}\mathrm{E}$$$$\mathbf{BC}\Rightarrow {3\mathrm{a}}^2\mathrm{x}+8\mathrm{y}+12\mathrm{a}=....\left(\mathrm{ii}\right)$$$$\mathrm{Solving}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right)\mathrm{we}\mathrm{get}\mathbf{C}$$$$\therefore \mathbf{The}\mathbf{required}\mathbf{area}=△\mathrm{ODC}+△\mathrm{OEC}$$$$=\frac{1}{2}\times \frac{2}{\mathrm{a}}\times 9\mathrm{a}+\frac{1}{2}\times \frac{3\mathrm{a}}{2}\times \frac{20}{\mathrm{a}}$$$$=9+15=24$$

Commented by Prithwish sen last updated on 01/Sep/19

Commented by mr W last updated on 01/Sep/19

$$correct!thankssir!$$

Commented by Prithwish sen last updated on 02/Sep/19

$$\mathrm{welcome}\mathrm{sir}.$$

Answered by MJS last updated on 01/Sep/19

$$\frac{op}{2}=1\Rightarrow p=\frac{2}{o}$$$$\frac{pq}{2}=2\Rightarrow q=2o$$$$\frac{qr}{2}=3\Rightarrow r=\frac{3}{o}$$$$A=\left(\begin{array}{c}o\\ 0\end{array}\right)B=\left(\begin{array}{c}0\\ \frac{2}{o}\end{array}\right)C=\left(\begin{array}{c}-2o\\ 0\end{array}\right)D=\left(\begin{array}{c}0\\ -\frac{3}{o}\end{array}\right)$$$$AB:y=-\frac{2}{o^2}x+\frac{2}{o}CD:y=-\frac{3}{2o^2}x-\frac{3}{o}$$$$AB\cap CD=E=\left(\begin{array}{c}10o\\ -\frac{18}{o}\end{array}\right)$$$$\mid OA\mid =o$$$$\mid OD\mid =\frac{3}{o}$$$$\mid AD\mid =\frac{\sqrt{o^4+9}}{o}$$$$\mid AE\mid =\frac{9\sqrt{o^4+4}}{o}$$$$\mid DE\mid =\frac{5\sqrt{4o^4+9}}{o}$$$$\mathrm{area}OAED=\mathrm{area}OAD+\mathrm{area}ADE=$$$$=\frac{3}{2}+\frac{45}{2}=24$$

Commented by mr W last updated on 01/Sep/19

$$thankssir!$$

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