Conic Sections Circles Ellipse Hyperbolas Parabolas.

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Presentation transcript:

Conic Sections Circles Ellipse Hyperbolas Parabolas

Tricks to looking at an equation and knowing what the shape will look like: Ellipse – you have 2 squared terms that are added together Circle – you have 2 squared terms with the same coefficient and are added together Hyperbola – 2 squared terms that are subtracted Parabola – 1 square term

Identify the conic shape of each equation. x 2 + 6x – y + 5 = 0 4x 2 + y 2 – 8x – 2y = -1 y 2 – 2x 2 + 2x + 2y = 9

CIRCLES

CIRCLE FORMULA (x – h) 2 + (y – k) 2 = r 2 Center: (h, k) Radius: r

Example 1-2 Write the standard form of the equation of the circle given the center and the radius. 1.(0, 0); √6 2.(3, -2); 7

Examples 3-5 Find the radius and the coordinates of each circle. 3.(x + 3) 2 + y 2 = 16 4.(x + 4) 2 + (y – 7) 2 = 7 5.2(x – 3) 2 + 2(y – 4) 2 = 8

Example 6 Graph the circle with a center of (2,-1) and a radius of 3.

Example 7 2x 2 + 2y 2 – 4x + 12y – 18 = 0 a.Write the standard form for the circle. b.Find the radius and the center of the circle. c.Graph the equation.

Real World Application: Seismology Portable autonomous digital seismographs (PADSs) are used to investigate the strong ground motions produced by the aftershocks of large earthquakes. Suppose a PADS is deployed 2 miles west and 3.5 miles south of downtown Olympia, Washington, to record the aftershocks fo a recent earthquake. While there, the PADS detects ad records the seismic activity of another quake located 24 miles away. What are all the possible locations of this earthquake’s epicenter? -Write an equation for all possible points. -Graph the equation.

Activity Take out the food/object you brought with you to class. Find the radius of your circle. First, find the center (you choose the coordinates). Then, measure the diameter and find the radius. Write the equation for your circular object. Graph your circle.

Practice Problems