Parabola y² = 4x, the y-axis and the line y = 3परवलय y² = 4x, y-अक्ष और रेखा y = 3Parabola y² = 4x, y-axis aur line y = 3

NCERT Exercise 8.1, Q4 · Class 12 Maths · Chapter 8 · interactive diagram

Parts and what they mean

• x-axis (x-अक्ष) — The horizontal number line; inputs x are read here.
• y-axis (y-अक्ष) — The vertical number line; outputs y = f(x) are read here.
• Origin O(0, 0) (मूल बिंदु O(0, 0)) — Where the two axes cross.
• Parabola y^2 = 4x (परवलय y^2 = 4x) — This is y^2 = 4ax with a = 1; it opens to the right, vertex at O. Solve for x: x = \frac{y^2}{4}.
• Line y = 3 (रेखा y = 3) — The top boundary: upper limit y = 3.
• Meeting point \left(\frac{9}{4}, 3\right) (मिलन बिंदु \left(\frac{9}{4}, 3\right)) — Put y = 3 in y^2 = 4x: 9 = 4x, so x = \frac{9}{4}.
• Horizontal strip (क्षैतिज पट्टी) — Length x = \frac{y^2}{4} (from the y-axis to the parabola), height dy.
• Required region (अभीष्ट क्षेत्र) — Area = \int_0^3 \frac{y^2}{4}\,dy = \left[\frac{y^3}{12}\right]_0^3 = \frac{9}{4} (option B).

Original diagram drawn by Simple Learning Hub, based on NCERT Exercise 8.1, Q4. Report a mistake