Question

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

• A. $x-y-1=0$
• B. $x-y+3=0$
• C. $x-y+5=0$
• D. $x-y-5=0$

Answer 1

The correct option is C $x-y+5=0$

$x^2+y^2+x-y=0$
$\Rightarrow 2x+2y\frac{dy}{dx}+1-\frac{dy}{dx}=0$
$\Rightarrow (2y-1)\frac{dy}{dx}=-(2x+1)\Rightarrow (\frac{dy}{dx}{)}_{0,0}=1$
$\therefore$ Required Line slope = 1, point = (-2, 3)
$\therefore$ Equation of Line is
$y-3=x+2\Rightarrow x-y+5=0$