Question

The length of the subtangent at $P(1,-3)$ on the curve

$x^2+xy+y^2=7$ is equal to

Answer 1

Given, $x^2+xy+y^2=1$

On differentiating w.r.t $x$, $2x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}=0$

$\Rightarrow \frac{dy}{dx}=-\frac{(2x+y)}{x+2y}$
Slope of tangent at given point $=\frac{-(2-3)}{1-6}=\frac{-1}{5}$

Length of subtangent is: $\left|\frac{y_1}{m}\right|=15$ units.