Intro to Conics

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## Intro to Conics

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**A conic section is a curve formed by the intersection of**_________________________ a plane and a double cone.**(h , k)**r Circles The set of all points that are the same distance from the center. Standard Equation: With CENTER: (h, k) & RADIUS: r (square root)**®**- h , ) ( 2 8 Example 1 -h r² -k Center: Radius: r 9 ( ) k ,**Example 2**Center ? Radius ?**Standard Equation:**(h , k) a b Ellipse Basically an ellipse is a squishedcircle Center: (h , k) a: major radius (horizontal), length from center to edge of circle b: minor radius (vertical), length from center to top/bottom of circle * You must square root the denominator**This must equal 1**a² b Example 3 2 Center: (-4 , 5) a: 5 b: 2**Standard Equations:**OR vertex Parabola vertex We’ve talked about this before… a U-shaped graph This equation opens left or right This equation opens up or down HOW DO YOU TELL…LOOK FOR THE SQUARED VARIABLE • Vertex: (h , k) • If there is a negative in front of the squared variable, then it opens down or left. • If there is NOT a negative, then it opens up or right.**Example 5**Example 4 opens down What is the vertex? How does it open? (-2 , 5) opens right What is the vertex? How does it open? (0 , 2)**Standard Equations:**OR Hyperbolas What I look like…two parabolas, back to back. This equation opens up and down This equation opens left and right Have I seen this before? Sort of…only now we have a minus sign in the middle (h , k) Center: (h , k)**Example 6**Center: (-4 , 5) Opens: Left and right**What am I?**Name the conic section and its center or vertex.