Q16 of 29 Page 1

Find the equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1) where x1 = 2 and y1 > 0.

OR


Find the intervals in which the function f(x) = is


(a) Strictly increasing,


(b) Strictly decreasing.

∵ P () = (2 lies on


)






Since its been given that


So, .


∴ P = (2, 3)


…… (i)




Slope of tangent =


Slope of normal =


Equation of tangent is,


(y – 3) = (x – 2)


27y – 81 = – 32x + 64


Equation of normal is,


(y – 3) = (x – 2)


32y – 96 = 27x – 54


27x – 32y – 54 + 96 = 0


27x – 32y – 54 + 96 = 0


27x – 32y + 42 = 0


OR




f(x) is strictly increasing if f'(x)>0,



∴


f(x) is strictly decreasing if f'(x) <0


∴ .

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