The tangent at any point `(x , y)`of a curve makes an angle `tan^(-1)(2x+3y)`with x-axis. Find the equation of the curve if itpasses through (1,2).A. ` 6x+9y +2 = 26 e^(3(x-1))`B. ` 6x- 9y +2 = 26 e^(3(x-1))`C. ` 6x + 9y -2 = 26 e^(3(x-1))`D. ` 6x - 9y -2 = 26 e^(3(x-1))`

The tangent at any point `(x , y)`of a curve makes an angle `tan^(-1)(

1.	The tangent at any point `(x , y)`of a curve makes an angle `tan^(-1)(2x+3y)`with x-axis. Find the equation of the curve if itpasses through (1,2).A. ` 6x+9y +2 = 26 e^(3(x-1))`B. ` 6x- 9y +2 = 26 e^(3(x-1))`C. ` 6x + 9y -2 = 26 e^(3(x-1))`D. ` 6x - 9y -2 = 26 e^(3(x-1))`
Answer» Correct Answer - a Given , `(dy)/(dx) = tan theta = 2x +3y` Put ` 2x + 3y = z rArr 2 +3 (dy)/(dx) = (dz)/(dx)` ` rArr (dy)/(dx) = ((dz)/(dx) - 2 ) 1/3 ` ` :. (dz)/(dx) - 2 = 3z rArr (dz)/(3z + 2) = dx` On integrating , we get `(log (3z+2))/3 = x+C` ` rArr (log (6x + 9y +2))/3 = x=C` Since , it passes through (1,2) ` :. (log (6+18+2))/3 = 1+C rArr C = (log 26)/3 -1` ` :. (log (6x +9y+2))/3 = x + (log 26)/3 -1` ` rArr log ((6x+9y+2)/26) = 3 ( x-1)` ` rArr 6x + 9y +2 = 26 e^(3(x-1))`

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The tangent at any point `(x , y)`of a curve makes an angle `tan^(-1)(2x+3y)`with x-axis. Find the equation of the curve if itpasses through (1,2).A. ` 6x+9y +2 = 26 e^(3(x-1))`B. ` 6x- 9y +2 = 26 e^(3(x-1))`C. ` 6x + 9y -2 = 26 e^(3(x-1))`D. ` 6x - 9y -2 = 26 e^(3(x-1))`

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