![]() ![]() “a” represents the horizontal distance from the centre to the edge of the ellipse. (x + 2)2 + y 2 = 49 Domain: -9 ≤ x ≤ 5 Range: -7 ≤ y ≤ 7Ĭonics Lesson 1 Part III- Ellipses (x - h)2 (y - k)2 Ellipses: The equation of an ellipse is given by = 1, + a2 b2 (h, k) is the centre of the ellipse. When writing the domain & range for an enclosed shape, we use “in-between notation”ĭomain: Leftmost Value ≤ x ≤ Rightmost Value Range: Bottom Value ≤ y ≤ Top Value For the circle in this question: Domain: 0 ≤ x ≤ 6 (Read as “the domain is between zero and six”) Range: -7 ≤ y ≤ -1 (Read as “the range is between negative seven and negative one”)Ĭonics Lesson 1 Part II - Circles Questions: For each of the following graphs, write the equation, then state domain & range:Ĭonics Lesson 1 Part II - Circles Questions: For each of the following equations, draw the graph and state domain & range:Ĭonics Lesson 1 Part II - Circles Answers: 2 2 1. (x - 3) becomes zero when x = 3 (y + 4) becomes zero when y = -4 ![]() Quick Tip: An easy way to read off the centre is to use values for x and y that make each bracket go to zero. (Remember, you’re given r2 and you just want r.) 2 The radius can be found by taking the square root of the number on the right side. To draw the graph of a circle from a standard form equation, first draw a dot at the centre of the circle. Finally, plug the h, k, and r values into the standard form equation and you’ll have the equation of the graph! Next, determine the radius, which is 4 units. The first thing you should do when given a circle is write down the coordinates of the centre. A hyperbola is produced when the plane passes through both nappes, between the central axis and generator.Ī parabola is produced when the plane passes through one nappe parallel to the generator.Īn ellipse is produced when the plane passes through one nappe only, between the generator and perpendicular.Ī circle is produced when the plane passes through one nappe only, perpendicular to the central axis.Ĭonics Lesson 1 Part II - Circles Circles: The standard form of a circle is given by the equation (x - h)2 + (y - k)2 = r 2, where (h, k) is the centre of the circle and r is the radius.Įxample 1: Given the following graph, write the equation. In theory, the double napped cone extends forever up & down. The point at the centre is called the vertex. The vertical line down the middle is called the central axis, and the diagonal sides are called generators. The shape to the right is a double napped cone. It is possible to create each of these shapes by passing a plane through a three dimensional double napped cone. Conics Lesson 1 Part I – The Double – Napped Cone Conic Sections: There are 4 main conic sections: circle, ellipse, parabola, and hyperbola. ![]()
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