Question

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.

Options

• An ellipse

• Parabola

• Circle

• Rectangular hyperbola

Answer 1

The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is rectangular hyperbola.

Explanation:

Since, the slope of the tangent to the curve = x : y

∴ `("d"y)/("d"x) = x/y`

⇒ ydy = xdx

Integrating both sides, we get

`int "y"  "d"y = int x  "d"x`

⇒ `y^2/2 = x^2/2 + "c"`

⇒ y² = x² + 2c

⇒ y² – x² = 2c = k which is rectangular hyperbola.