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Question Number 95206 by hardylanes last updated on 23/May/20

$$findtheequationofthestraightlinewhich$$$$passesthroughthepointofintersertionof$$$$thelines4x+3y+19=0and12x-5y+3=0$$$$andhasay\mathrm{\_}interceptof2$$

Commented by PRITHWISH SEN 2 last updated on 24/May/20

$$\mathrm{Let}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{be}$$$$4\mathrm{x}+3\mathrm{y}+19+\mathbf{k}(12\mathrm{x}-5\mathrm{y}+3)=0.....\left(\mathrm{i}\right)$$$$\because \left(\mathrm{i}\right)\mathrm{passes}\mathrm{through}(0,2)$$$$\therefore 6+19+\mathbf{k}(-10+3)=0$$$$\Rightarrow \mathrm{k}=\frac{25}{7}$$$$\therefore \mathrm{the}\mathrm{req}.\mathrm{equ}.\mathrm{is}$$$$4\mathrm{x}+3\mathrm{y}+19+\frac{25}{7}(12\mathrm{x}-5\mathrm{y}+3)=0$$$$41\mathbf{x}-13\mathbf{y}+26=0$$

Answered by bobhans last updated on 24/May/20

$$\mathrm{the}\mathrm{point}\mathrm{intersection}\mathrm{of}\mathrm{the}\mathrm{lines}\mathrm{is}(-\frac{13}{7},-\frac{27}{7})$$$$\mathrm{and}\mathrm{y}-\mathrm{intercept}2\Rightarrow \mathrm{The}\mathrm{equation}\mathrm{of}$$$$\mathrm{straight}\mathrm{line}\mathrm{with}\mathrm{slope}=\frac{2+\frac{27}{7}}{0+\frac{13}{7}}=\frac{41}{13}$$$$.\mathrm{so}\mathrm{the}\mathrm{eq}\mathrm{of}\mathrm{line}$$$$\mathrm{is}\Rightarrow 41\mathrm{x}-13\mathrm{y}=-26$$

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