Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is expressed as a rational p q (where p and q are i

Question

Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is expressed as a rational p q (where p and q are in their lowest form), then find (p+q) .

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Correct answer: 19

Let P(x, y) be any point on the curve C . Now, dy dx = 1 y Since the curve passes through M(2,2) , so k=0 y^2=2 x Hence required area =2 ₀^2 2 x dx =2 2 2 3 ( x ^ 3 / 2 )₀^2= 4 3 2 2 2 = 16 3 (square unit) p+q=19

Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is expressed as a rational p q (where p and q are in their lowest form), then find (p+q) .

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