Warm up! Graph the following equation: x y 9 2 2 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 For your exams… …the average was a 71%… …the median was an 83%… …a few people haven’t taken it yet… …and the folks who did their HW scored about 10% better than those who did not! The Wørd Section 9.0 Completing the Square and Circles So I have been all fire and brimstone… Conic Sections A conic section is the set of all points formed by the intersection of a plane and a double-napped cone. …for a few months now. Ellipses The planets travel in elliptical orbits. …not circular ones. And I think it’s because… Hyperbolas Comets can be slowed by the sun’s gravity… …I’m in a bit of a mid-life crisis. Conic Equations x 4 x 4 y 2 y 1 17 2 2 3x 4 y 8 y 4 12 2 2 Conic sections are loci (the plural of locus). A locus is the set of all points that satisfy a given relation. A locus may be a function, but conic sections are not. I’m 30. Conic Equations x 4 x 4 y 2 y 1 17 2 2 3x 4 y 8 y 4 12 2 2 ( x 2) ( y 1) 17 2 2 x ( y 1) 1 4 3 2 2 I thought that maybe… Complete the square for the given quadratic. x 6x 2 …just maybe… Complete the square for the given quadratic. y 8y 2 …I’d have won the lottery by now… Complete the square for the given quadratic. a 5a 2 …I’d be driving a Nissan GT-R… Complete the square for the given quadratic. z 12 z 2 …the Blues would’ve won a Cup… Complete the square for the given quadratic. 4 x 16 x 2 …I’d be living on a beach in Mexico… Complete the square for the given quadratic. 3x 6 x 2 …I’d own a 5000 ft vacation home… Complete the square for the given quadratic. 7y 7y 2 …on the moon… Complete the square for the given quadratic. 5 z 35 z 2 …and have won a Nobel Prize… Complete the square for the given quadratic. y 2y 2 …in awesome. Complete the square for the given quadratic. 9 y y 2 But no. Circles A circle is the set of all points equidistant from a given point called the center. The equation for a circle in standard form with center (h, k) and radius r is given by the equation: ( x h) ( y k ) r 2 2 2 Graph the given circle. x 8x y 4 y 16 2 2 All those lotto tix have been a waste… 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 Graph the given circle. x y 10 y 0 2 2 …I drive a Hyundai… 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 …the Blues haven’t been to the Finals in 40 years… Graph the given circle. x y 2 x 2 y 47 2 2 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 Find and graph the equation of the circle with the given center and radius. center (5, 2) r 3 …I still live in the LOU… 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 Ditto on the directions. …no one lives on the moon… center (2, 9) r 1 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 Graph the given circle. x 4 x y 6 y 12 2 2 …and I keep coming in 2nd… 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 Graph the given circle. …for that Nobel Prize. x 12 x y 14 y 76 0 2 2 8 6 4 2 -10 -5 5 -2 -4 -6 -8 10 And your homework! 9.0 in the packet!