Area of the circle x² + y² = a²: four equal quartersवृत्त x² + y² = a² का क्षेत्रफल: चार बराबर चौथाई भागCircle x² + y² = a² ka area: chaar barabar quarter

NCERT Example 1 (Fig 8.5, 8.6) · 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.
• Circle x^2 + y^2 = a^2 (वृत्त x^2 + y^2 = a^2) — Centre O, radius a. It is symmetric about both axes, so whole area = 4 \times quarter.
• Region AOBA (first quadrant) (क्षेत्र AOBA (प्रथम चतुर्थांश)) — Here y = +\sqrt{a^2 - x^2} (y is positive). Its area is \int_0^a \sqrt{a^2 - x^2}\,dx = \frac{\pi a^2}{4}.
• Vertical strip (ऊर्ध्वाधर पट्टी) — Height y = \sqrt{a^2 - x^2}, width dx; x runs from 0 to a.
• Horizontal strip (क्षैतिज पट्टी) — Length x = \sqrt{a^2 - y^2}, height dy; y runs from 0 to a. Same answer \pi a^2.
• Point A(a, 0) (बिंदु A(a, 0)) — Where the circle meets the positive x-axis: upper limit x = a.
• Point B(0, a) (बिंदु B(0, a)) — Where the circle meets the positive y-axis: upper limit y = a for horizontal strips.

Original diagram drawn by Simple Learning Hub, based on NCERT Example 1 (Fig 8.5, 8.6). Report a mistake