Question

The length of the subtangent to the curve $x^2 + xy + y^2 = 7$ at $ (1, - 3)$ is

• A. 3
• B. 5
• C. 15
• D. $\frac {3} {5}$

Answer 1

Answer: (C)

$x^{2}+xy+y^{2}=7$
$\Rightarrow 2x + x \frac{dy}{dx}+y\cdot1+2y \frac{dy}{dx}=0$
$\Rightarrow \left(x + 2y\right) \frac{dy}{dx} = -\left(2x+y\right)$
$\Rightarrow \frac{dy}{dx} = -\frac{2x+y}{x+2y}$
At $\left(1.3\right) \frac{dy}{dx} =- \frac{2-3}{1-6} = -\frac{1}{5}$
Length of the subtangent $= \frac{y}{\frac{dy}{dx}}=\frac{3}{-\frac{1}{5}} = 15$