Question

If curve not passing through origin, having slope is ratio of its x and y co-ordinate, then it represent __________ curve.

• A. Rectangular hyperbola
• B. Circle
• C. Line
• D. Ellipse

Answer 1

Answer: (A)

Rectangular hyperbola

Rectangular hyperbola
Slope of the tangent$=\frac{dy}{dx}$
Here $\frac{dy}{dx}=\frac{x}{y}$(Given)
$\therefore ydy=xdx$
$\therefore \int xdx=\int ydy$
$\therefore \frac{x^2}{2}=\frac{y^2}{2}+c$
$\therefore x^2-y^2=2c$
Which represents rectangular hyperbola.