Question

A curve is such that the area of the region bounded by the coordinates axes, the curve and the ordinate of any point on it is equal to the cube of that ordinate the curve represent.

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

Answer 1

The correct option is C a parabola

Given that,

The curve and the coordinate of any point on its equal to the cube of

that ordinates.

Let (h, k) be point on it is equal to the cube of that ordinate.

Given the area of the region bounded by the co-ordinate axis in above figure.

We know that the area of rectangle is

$Area=length\times breath$

But Given that ,

Ordinate of point $=k$

$h\times k=k^3$ (given function )

$h=k^2$

Hence it represent the parabola.

hence option $\left(C\right)$ is correct.