5.02a - Circle at Origin | High School - Edubirdie

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5.02 The Circle 5.02A – THE CIRCLE AT THE ORIGIN Circle Centred at the Origin • The circle is a locus of points equidistant from a fixed point: the centre. Rule of Circle Centred at the Origin • Rule obtained from Pythagorean theorem: r y x 2 2 𝑥 +𝑦 = 𝑟 2 Example • Find the equation of a circle with centre (0,0) and radius of 2: 2 𝑥 2 𝑦 2 𝑟 + = 2 2 2 𝑥 + 𝑦 = (2) 2 2 𝑥 +𝑦 =4 • Note: The rule has two variables, BOTH of degree 2 Let’s Visualize 𝑥2 + 𝑦2 = 4 radius = 2 So: A(2,0) B(0, 2) C(-2,0) D(0,-2) Test A 2 2+ 0 2= 4 • Test D 0 2 + −2 2 = 4 • • • • • • • • B C A D Radius and Analytic Geometry From our diagram, we can also see that the radius is the distance between the centre and any given point on the locus. 𝑟 = 𝑑𝐶𝑃 = (𝑥 − 0)2 +(𝑦 − 0)2 𝑟 = 𝑑𝐶𝑃 = 𝑥2 + 𝑦2 Inequalities Consider an inequality based on the relation to the radius – Bigger than Radius? 𝑥 2 + 𝑦 2 > 𝑟 2 • Shade outside the figure – Smaller than Radius? 𝑥 2 + 𝑦 2 ≤ 𝑟 2 • Shade inside the figure • Rule for solid vs dotted line still true ( ≥ vs > ) Homework • Visions 2 • P176: 1ace, 2ace, 5ab, 7ae, 9ad

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