What is the area of the parabola y2 = x bounded by its latus rectum?

\(\dfrac{1}{12}\) square unit

\(\dfrac{1}{6}\) square unit

\(\dfrac{1}{3}\) square unit

None of the above

What is the area of the parabola y2 = x bounded by its latus rectum? Correct Answer \(\dfrac{1}{6}\) square unit

Concept:

Equation of parabola along X-axis:

(y)² = ±4ax, focus (±a, 0)

Calculation:

Here, parabola y² = x = 4 (1/4) x

Hence a = 1/4,

Now focus = (a , 0)

_0^\frac{1}{4}\\ =2\\ =\frac{4}{3}(\frac{1}{4})(\frac{1}{2})\\ =\frac{1}{6}\)

Hence, option (2) is correct.

Feb 20, 2025

Related Questions