The slope of tangent to the curve r...
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The slope of tangent to the curve represented parametrically by the equations x = 2 - 3t + 1 and y= 22 + 3t - 4 at M(-1,10) is - (A) 5 (B) 9 (C)7 (D) 11

JEE/Engineering Exams
Maths
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slope of tangent ( =frac{d y}{d x}=frac{d y / d t}{d x / d t} ) ( frac{d y}{d t}=4 t+3, frac{d x}{d t}=2 t-3 ) ( left.frac{d y}{d x}right|_{(-1,10)}=y cdot frac{4++3}{2 t-3} ) ( y=1 quad y=-1 Rightarrow quad t^{2}-3 t+1=-1 ) ( Rightarrow quad quad Rightarrow quad t^{2}-3 t+2=0 ) [ begin{array}{c} (t-1)(t-2)=0 t=1,2 2 t^{2}+3 t-4=10 2 t^{2}+3 t-14=0 (t-2)(2 t+7) end{array} ] ( t=2, t=-7 / 2 ) now putting ( t=2 quad ) in ( frac{d y}{d x} ) [ left.frac{d y}{d n}right|_{(-1,10)}=frac{p+3}{4-3}=11 ]
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