Question

The equation of the 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)

$2x - y + 4 = 0$

Answer 2

$x^{2} = - 4y$ ⇒ $2x = - 4\frac{dy}{dx}$ ⇒ $\frac{dy}{dx} = \frac{- x}{2}$ ⇒ $\left( \frac{dy}{dx} \right)_{( - 4, - 4)} = 2$.

We know that equation of tangent is

$(y - y_{1}) = \left( \frac{dy}{dx} \right)_{(x_{1},y_{1})}(x - x_{1})$ ⇒ $y + 4 = 2(x + 4)$

⇒ $2x - y + 4 = 0$.