MATH 140 Lecture Notes - Lecture 37: Ellipse

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Denny Gulick

Document Summary

Math140 lecture 37 conic sections (parabolas and ellipses) Let p be a point not on a given line l. then the collection of points equidistant from p and l form a parabola. Example: let p = (0, c, let the line l be y = -c, let (x, y) be a point on the parabola. X2+( y c)2= y+c x2+( y c)2=( y+c)2 x2=4cy: vocabulary: The point (0, c) is the focus. The line x = -c is the directrix. The point (0, 0) is the vertex. Example: ex1: x2+2 x 12 y+25=0 . Complete the square: (x2+2 x+1) 12 y+24=0 ( x+1)2=12( y 2) Directrix: (y = -1: ex2: y2 4 y +2x=6 y2 4 y+4 +2x =10 ( y 2)2= 2 x+10= 2(x 5) Let p1 and p2 be distinct; let k > 0. The point p is such that |p1p| + |p2p|