Question

The slope of the tangent to a curve at a point is twice to that of the line joining that point to the origin, then the curve is –

• A. A circle
• B. A parabola
• C. An ellipse
• D. A hyperbola

Answer 1

Answer: (B)

A parabola

Answer 2

Let point (x, y)

\ $\frac{dy}{dx}$ = 2 $\left( \frac{y}{x} \right)$

Ž $\frac{dy}{y}$ = 2. $\frac{dx}{x}$

Ž log y = 2.log x + log c

Ž $\begin{matrix} y = cx^{2} \end{matrix}$ Ž It is a parabola