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)

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