The equation of the normal to the curve $y = ax + \frac{b}{x}$ at the point $(2, 7)$ is \(2y + 4

Question

The equation of the normal to the curve $y = ax + \frac{b}{x}$ at the point $(2, 7)$ is $2y + 4x = 22$, find the value of $a$ and of $b$. Given that the normal meets the curve again at $P$, find the coordinates of $P$.

Accepted Answer

(a) $a=2$, $b=6$ (b) $P=\left(\frac34,\frac{19}{2}\right)$

Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point

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