Question

Find the equation of a line passing through $(-2,3)$ and parallel to tangent at origin for the circle $x^2+y^2+x-y=0$

• A. $x-2y+5=0$
• B. $x-4y+3=0$
• C. $x-y+5=0$
• D. $2x-y+6=0$

Answer 1

Answer: (C)

$x-y+5=0$

Given,$x^2+y^2+x-y=0$
Differentiating w.r.t $x$, we get
$2x+2y\frac{dy}{dx}+1-\frac{dy}{dx}=0$
$\Rightarrow \frac{dy}{dx}=\frac{1+2x}{1-2y}$
Thus slope of the tangent at origin is, $m={\left(\frac{dy}{dx}\right)}_{(0,0)}=1$
Hence required line through $(-2,3)$ is, $(y-3)=1(x+2)\Rightarrow x-y+5=0$