Question

If tangents are drawn from the origin to the curve $y=\sin x$, then their points of contact lie on the curve

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

Answer 1

Answer: (C)

The tangent at $\left(x_1,\sin x_1\right)$ is $y-\sin x_1=\cos x_1\left(x-x_1\right)$
It passes through the origin.
$\sin x_1=x_1\cos x_1=x_1\sqrt{1-{\sin }^2{x}_1}$
$y_1{}^2={\sin }^2{x}_1=x_1^2\left(1-y_1^2\right)$
$\Rightarrow \left(x_1{y}_1\right)\left(x_1{y}_1\right)$ lies on the curve
$y^2=x^2\left(1-y^2\right)$
$\Rightarrow x^2-y^2=x^2{y}^2$