Question

The equation of a normal 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 Normal slope = 1, point = (-2, 3)
$\therefore$ Equation of Normal is
$y-3=x+2\Rightarrow x-y+5=0$