Question

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

• A. $2x+y+4=0$
• B. $2x–y–6=0$
• C. $2x+y–4=0$
• D. $2x–y+4=0$

Answer 1

The correct option is D

$2x–y+4=0$

Explanation for correct answer:

We have, $x^2=–4y$

On differentiating with respect to $x$ we get

$$\begin{gathered} \Rightarrow 2x=–4(\frac{dy}{dx}) \\ \Rightarrow \frac{dy}{dx}=\frac{-x}{2} \end{gathered}$$

The equation of the tangent, is given as:

$$\begin{gathered} \Rightarrow (y–y_1)=\left(\frac{dy}{dx}\right)(x–x_1) \\ \Rightarrow y+4=2\left(x+4\right)[\mathrm{Given},(-4,-4\left)\right] \\ \Rightarrow 2x-y+4=0 \end{gathered}$$

Hence, the correct answer is option (D)