Question

A curve is such that the area of the region bounded by the co-ordinate axes, the curve & the ordinate of any point on it is equal to the cube of that ordinate. The curve represents

• A. a pair of straight lines
• B. a circle
• C. a parabola
• D. an ellipse

Answer 1

Answer: (C)

$\underset{0}{\overset{x}{\int }}f(x)dx=y^3$

Differentiating
$f(x)=3y^2\cdot \frac{dy}{dx}$
$y=3y^2\frac{dy}{dx}\Rightarrow y=0\text{ (rejected) }$
$\text{ or }3ydy=dx$
$\frac{3y^2}{2}=x+c\Rightarrow \text{ parabola }\Rightarrow C$