Question

Tangents are drawn from the origin to the curve y = sin x. Their points of contact lie on the curve

• A. $x^2{y}^2=x^2+y^2$
• B. $x^2{y}^2=x^2-y^2$
• C. $x^2{y}^2=y+x$
• D. $XY=X+Y$

Answer 1

The correct option is B

$x^2{y}^2=x^2-y^2$

The given curve is y =sin x ....(1)
$\Rightarrow \frac{dy}{dx}=cosx$.
So,the equation of tangents through the origin (0,0) is
$y-0=\frac{dy}{dx}(x-0)=xcosx,\therefore \frac{y}{x}=cosx....\left(2\right)$
Squaring and adding equation (1) and (b), we get
$y^2+\frac{y^2}{x^2}=1.\therefore x^2{y}^2=x^2-y^2$
Hence (b) is the correct answer.