# A curve is such thatdy/dx = 5-8/x^2. The line 3y + x = 17 is the normal to the curve at the point P on thecurve. Given that the x-coordinate of P is positive, B) ﬁnd the equation of the curve

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### 1 Answer

From part A) we have found that the cordinates of P is (2,5).

http://www.enotes.com/homework-help/curve-such-that-dy-dx-5-8-x-2-line-3y-x-17-normal-451702

`y = 5x-8/x+C` Where C is constant.

This goes through point P. So the curve should satisfy x and y cordinates of P.

P = (2,5)

`5= 5xx2 – 8/2 +C`

`C= -1`

`y=5x-8/x-1`

*So the equation of the curve is;*

`y=5x-8/x-1`

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Please accept the correction for mistype.

`5 = 5xx2-8/2+C`

`5 = 10-4+C`

`C = -1`