Question

The equation of normal of $x^2+y^2-2x+4y-5=0$ at $(2,1)$ is

• A. $y=3x-5$
• B. $2y=3x-4$
• C. $y=3x+4$
• D. $y=x+1$

Answer 1

Answer: (A)

Given equation is
$x^2+y^2-2x+4y-5=0$
On differentiating, we get
$2x+2y\frac{dy}{dx}-2+4\frac{dy}{dx}=0$
$\Rightarrow (y+2)\frac{dy}{dx}=1-x$
$\Rightarrow {\left(\frac{dy}{dx}\right)}_{(2,1)}=\frac{1-2}{1+2}=\frac{-1}{3}$
$\Rightarrow -{\left(\frac{dx}{dy}\right)}_{(21)}=3$
Now, equation of normal is
$(y-1)=3(x-2)$
$y-1=3x-6$
$\Rightarrow y=3x-5$