11.1 Intro to Conic Sections & The Circle

What is a “Conic Section”? A curve formed by the intersection of a plane and a double right circular cone. We will study these in detail one at a time!

Circles : set of all points in a plane at a fixed distance from a fixed point (radius) (center) C(h, k) P(x, y) Center C(h, k) Any point on circle P(x, y) By distance formula: r standard form of a circle Check out the problems around the room. Work together and answer them all!

1)Find center & radius. x 2 + y 2 + 8x – 10y = 23 C(–4, 5) r = 8 2)Determine an equation of a circle congruent to the graph of x 2 + y 2 = 16 and translated 3 units right and 1 unit down. (x – 3) 2 + (y + 1) 2 = 16 3)The general form of a circle is x 2 + y 2 + Dx + Ey + F = 0. *In completing the square if r > 0  circle r = 0  degenerate circle / point circle r < 1  the empty set (not possible) Determine what 3x 2 + 3y 2 – 30x + 18y = 0 represents. empty set

4)Determine the equation of the circle that passes through these three points: (5, 3), (–1, 9), (3, –3). *Use x 2 + y 2 + Dx + Ey +F = 0 here’s a hint … for (5, 3): D + 3E + F = 0 x 2 + y 2 + 4x – 4y – 42 = 0  (x + 2) 2 + (y – 2) 2 = 50 5)Determine an equation of a circle that satisfies the center at (2, 3) tangent to line 5x + 6y = 14. *remember! Distance from a point to a line (x 1, y 1 ) d Ax + By + C = 0

Homework #1101 Pg 538 #5, 7, 15, 21, 22, 24–26, 30–32, 34, 36, 38, 41, 45, 47, 49, 51