Question

The equation of tangent at $(-4,-4)$ on the curve $x^2=-4 y$ is

• A. $2 x+y+4=0$
• B. $2 x-y-12=0$
• C. $2 x+y-4=0$
• D. $2 x-y+4=0$

Answer 1

Answer: (D)

$ x^2=-4 y \Rightarrow 2 x=-4 \frac{d y}{d x}$
$ \Rightarrow \frac{d y}{d x}=\frac{-x}{2} $
$ \Rightarrow\left(\frac{d y}{d x}\right)_{(-4,4)}=2$
We known that equation of tangent is, $\left(y-y_1\right)=\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}\left(x-x_1\right)$
$\Rightarrow y+4=2(x+4) \Rightarrow 2 x-y+4=0$