Question

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

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

Answer 1

The correct option is C $15$

We have,

$x^2+xy+y^2=7$

On differentiating w.r.t $x$, we get

$2x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}=0$

Since, the given point $(1,-3)$

Therefore,

$2\times 1+\frac{dy}{dx}-3+2\times -3\frac{dy}{dx}=0$

$2+\frac{dy}{dx}-3-6\frac{dy}{dx}=0$

$-1-5\frac{dy}{dx}=0$

$\frac{dy}{dx}=-\frac{1}{5}$

We know that the length of the sub-tangent

$=\left|\frac{y}{\frac{dy}{dx}}\right|$

$=\left|\frac{-3}{-\frac{1}{5}}\right|$

$=15$

Hence, this is the answer.