Question

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

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

Answer 1

Answer: (D)

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