Question

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

Answer 1

According to the question,
\[\frac{dy}{dx} = \frac{1}{2y}\]
\[ \Rightarrow 2y dy = dx\]
Integrating both sides, we get
\[2\int y dy = \int dx\]
\[ \Rightarrow y^2 = x + C\]
Since the curve passes throught the point (4, 3), it satisfies the equation of the curve.
\[9 = 4 + C\]
\[ \Rightarrow C = 5\]
Putting the value of C in the equation of the curve, we get
\[ y^2 = x + 5\]