The slope of the tangent to the curve at any point is reciprocal of twice the ordinate of that point. The curve passes through the point `(4, 3)`. Determine its equation.

Answer

`y^2=x+5`

Explanation

According to the question,


`(dy)/(dx)=1/(2y)`


` 2ydy=dx`


integrating both sides we get


`int 2ydy=int dx`


`rArr (2y^2)/2=x+c`


`rArr y^2=x+c`


Since the curve passes through `(4,3)` which is `x=4` and `y=3` then,


...