Question

The curve that passes through the point (2, 3), and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact is given by :

• A. $2y - 3x = 0$
• B. $y = \frac{6}{x}$
• C. $x^2 + y^2 = 13$
• D. $\left(\frac{x}{2}\right)^{2}+\left(\frac{y}{3}\right)^{2} = 2$

Answer 1

Answer: (B)

$y = \frac{6}{x}$

Answer 2

$Y - y = \frac{dy}{dx} \left(X-x\right)$ X-intercept is$\left(x-\frac{y}{dy / dx}, 0\right)$ Y- intercept is $\left(0, y - \frac{xdy}{dx}\right)$ According to statment $x-\frac{y}{dy / dx} = 2x$ and $y - \frac{xdy}{dx} = 2y$ $\frac{-y}{\frac{dy}{dx}} = x \quad\quad \frac{-xdy}{dx} = y$ $\frac{dx}{x}+\frac{dy}{y} = 0$ $\ell ny = -\ell nx + \ell nc$ $y = \frac{c}{x} \Rightarrow c = 6$ Hence $y = \frac{6}{x}$