Question

Let $M$ and $N$ be the number of points on the curve $y^5–9xy+2x=0$, where the tangents to the curve are parallel to x-axis and y-axis, respectively. Then the value of $M+N$ equals ________.

• A. 2.00
• B. 2.0
• C. 2

Answer 1

Answer: (A), (B), (C)

Here equation of curve is $y^5–9xy+2x=0$ …(i)
On differentiting $5y^4\frac{dy}{dx}-9y-9x\frac{dy}{dx}+2=0$

$\therefore \frac{dy}{dx}=\frac{9y-2}{5y^4-9x}$

When tangents are parallel to x axis then $9y-2=0$

$\therefore M=1$

For tangent perpendicular to x -axis
$5y^4-9x=0$ ...(ii)

From equation (i) and equation (ii) we get only one point.

$\therefore N=1$.
$\therefore M+N=2$.