Question

The slope of the normal to the curve x² + y² − 2x + 4y − 5 = 0 at (2, 1) is _________________.

Answer 1

The equation of given curve is

x² + y² − 2x + 4y − 5 = 0

Differentiating both sides with respect to x, we get

$2x+2y\frac{dy}{dx}-2+4\frac{dy}{dx}-0=0$

$\Rightarrow \left(2y+4\right)\frac{dy}{dx}=2-2x$

$\Rightarrow \frac{dy}{dx}=\frac{1-x}{y+2}$

∴ Slope of normal at (2, 1)

$=-\frac{1}{{\left({\displaystyle \frac{dy}{dx}}\right)}_{\left(2,1\right)}}$

$=-\frac{1}{\left({\displaystyle \frac{1-2}{1+2}}\right)}$

$=-\frac{1}{\left(-{\displaystyle \frac{1}{3}}\right)}$

= 3

Thus, the slope of normal to the given curve x² + y² − 2x + 4y − 5 = 0 at (2, 1) is 3.


The slope of the normal to the curve x² + y² − 2x + 4y − 5 = 0 at (2, 1) is ___3___.