Questions from 8.5 and 8.6
CONIC SECTIONS
Conics got their name because they can be made by intersecting a plane with a double cone.
What is a circle?
Every point (x, y) on the circle is equidistant from
the center (h, k). That distance is the radius, r.
(x, y)
(h, k)
r
The standard equation of a circle with radius r and center (h, k) is
(x ­ h)2 + (y ­ k)2 = r 2
Find the equation of a circle with radius 7 and center (2, ­5)
Find the equation of a circle whose diameter has endpoints (­3, 4) and (5, 8).
How will you recognize you have a circle equation?
(x ­ 3)2 + (y + 2)2 = 7
Circle? 4x2 +4y2 ­ 20x ­ 20y + 52 = 0
This one did not form a circle. We ended up with a negative r2.
Not all equations like these will form circles. It actually will What is a parabola?
Up to now, you worked with a vertex. There is more to a parabola.
A parabola is the set of points EQUIDISTANT from a point and a line.
Let's build a parabola equation using the focus and the directrix.
Left or Right Opening Parabolas:
Upright or Upside Down Parabolas
Example: Graph the parabola y2 = 12x. Example: (x + 3)2 = ­8(y ­ 4)
Parabolic Cookers
http://britton.disted.camosun.bc.ca/pararay_lg.GIF
http://www.rpc.com.au/products/appliances/cookers/solar­cookers­faq.html
Reflective Properties of Parabolas
How can we tell we have a parabola?
Put the following equation in standard form and identify the vertex and the focus of the parabola. Which way does it open?
x2 + 4x + 6y ­ 2 = 0
A Satellite dish has a cross section that it a parabola. If the dish has a diameter of 10 feet and a depth of 4 feet, then where should the focus be located?