The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is (2x/y) represents

Question

The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is (2x/y) represents (A) Circle (B) Parabola (C) Ellipse (D) Hyperbola

Tardigrade Admin · Accepted Answer

Given, ((dy/dx)= (2x/y)) ⇒ y d y=2 x d x ⇒ ∫ y d y=∫ 2 x d x ⇒ y2 / 2=x2+A, where A is a constant. The above equation represents a hyperbola.

Q. The curve passing through the point $(1, 2)$ given that the slope of the tangent at any point $(x, y)$ is $\frac{2 x}{y}$ represents

Circle

Parabola

Ellipse

Hyperbola

Given, $(\frac{d y}{d x} = \frac{2 x}{y})$
$\Rightarrow y d y = 2 x d x$
$\Rightarrow \int y d y = \int 2 x d x$
$\Rightarrow y^{2} /2 = x^{2} + A$ , where $A$ is a constant.
The above equation represents a hyperbola.

Q. The curve passing through the point (1,2) given that the slope of the tangent at any point (x,y) is y2x​ represents