Conic Sections for Coffee Cup Project

For the equations graphed in "function grapher hofstra":

(((1/2)x^2)-3)/(x<3.2&x>-3.2);

((1/5)((23-(x^2))^(1/2))+1.18)/(x<3.2&x>-3.2);

((1/5)((5+(x^2))^(1/2))+1.1)/(x<3.2&x>-3.2);

((2/5)(16-x^2)^(1/2)-2.5)/(x<-1.9);

((2/5)(16-x^2)^(1/2)-2.5)/(x>1.9);

-(2/5)(16-x^2)^(1/2)-2.5;

((2/5)(16-x^2)^(1/2)-2.7)/(x<-1.8);

((2/5)(16-x^2)^(1/2)-2.7)/(x>1.8);

-(2/5)(16-x^2)^(1/2)-2.7;

((1/5)((23-(x^2))^(1/2))+0.95)/(x<2.5&x>-2.5);

(1.25-(x-2.5)^2)^(1/2)/(x>2.81);

-(1.25-(x-2.5)^2)^(1/2)/(x>2);

(2/3-(x-2.5)^2)^(1/2)/(x>2.72);

-(2/3-(x-2.5)^2)^(1/2)/(x>2.10);

(((x+1/2)^2+x)^(1/2)+2.5)/(x<-1&x>-2.5);

(-((x+1/2)^2+x)^(1/2)+2.5)/(x<-2&x>-2.18);

(((x+1/2)^2+x)^(1/2)+2.5)/(x>-1/2&x<1/2);

(-((x+1/2)^2+x)^(1/2)+2.5)/(x>-1/2&x<0.2);

(((x+2)^2+x)^(1/2)+2.5)/(x>-1&x<-1/2);

(-((x+2)^2+x)^(1/2)+2.5)/(x>-1&x<-4/5);

(((x-2.5)^2-x)^(1/2)+2.5)/(x>0.8&x<2);

(-((x-2.5)^2-x)^(1/2)+2.5)/(x>1.1&x<2);

(((x-0.5)^2-x)^(1/2)+2.5)/(x>1&x<2.7);

(-((x-0.5)^2-x)^(1/2)+2.5)/(x>1&x<2.15)

y=(1/2)x^2-3

The locus of coplanar points equidistant from the line y= -5 and the point (0,-1), and where the x-coordinate of any point on the parabola is greater than -3.2, and less than 3.2.

Vertex: (0,3) Equation of Directrix: y= -5 Coordinates of the focus: (0,-1)

((y-1.18)/√(23)/5)^2+(x/√(23))^2=1

The locus of coplanar points for which the sum of the distances between the fixed points (-4.7, 1.18) and (4.7, 1.18) is 9.6, and the x-coordinate of which is greater than -3.2 and less than 3.2, and include only the top half of the ellipse.

Center: (0, 1.18) r_x=4.8 r_y=.96 r_f=4.7 Foci: (-4.7, 1.18), (4.7, 1.18)

((y-1.1)/√(1/5))^2-(x/√5)^2=1

The set of points in a plane for each point of which the difference of the distances from the fixed points (0, -1.1), and (0, 3.46) is .89, and the domain is greater than -3.2, and less than 3.2.

Slope of asymptotes: 1/5, and -1/5

((y+2.5)/(8/5))^2+(x/4)^2=1

The locus of coplanar points for which the sum of the distances between the fixed points (3.7, -2.5) and (-3.7, -2.5) is 8; in the top half of the ellipse, the domain excludes all values ranging from -1.9 to 1.9.

Center: (0, -2.5) r_x=4 r_y=8/5 r_f=3.7 Foci: (3.7, -2.5), (-3.7, -2.5)

((y+2.7)/(8/5))^2+(x/4)^2=1

The locus of coplanar points for which the sum of the distances between the fixed points (3.7, -2.7) and (-3.7, -2.7) is 8; in the top half of the ellipse, the domain excludes all values ranging from -1.8 to 1.8.

Center: (0, -2.7) r_x=4 r_y=8/5 r_f=3.7 Foci: (3.7, -2.7), (-3.7, -2.7)

((y-0.95)/ (23)/5)^2+(x/√(23))^2=1

The locus of coplanar points for which the sum of the distances between the fixed points (3.7, -2.7) and (-3.7, -2.7) is 8; in the top half of the ellipse, the domain excludes all values ranging from -1.8 to 1.8.

Center: (0, 0.95) r_x=4.8 r_y=.96 r_f=4.7 Foci: (4.7, 0.95), (-4.7, 0.95)

y^2+(x-2.5)^2=1.25

The locus of coplanar points for which the distance from the fixed point (2.5, 0) is 1.1; in the top half of the circle the domain is greater than 2.81, in the bottom half, the domain is greater than 2.

Center: (2.5, 0) r=1.1

y^2+(x-2.5)^2=2/3

The locus of coplanar points for which the distance from the fixed point (2.5, 0) is .82; in the top half of the circle the domain is greater than 2.72, in the bottom half, the domain is greater than 2.1.

Center: (2.5, 0) r=.82

((x+1)/√(3/4))^2-((y-2.5)/√(3/4))^2=1

The set of points in a plane for each point of which the difference of the distances from the fixed points (-2.2, 2.5), and (.2, 2.5) is 1.7; in the top half of the parabola, the domain is limited to the ranges of -2.5 to -1, and -.5 to.5, and in the bottom half, the domain is limited to the ranges of -2.18 to -2, and -1.2 to .2.

Slope of asymptotes: 1 and -1.

-((y-2.5)/√(2.25))^2+((x+2.25)/√(2.25))^2=1

The set of points in a plane for each point of which the difference of the distances from the fixed points (-5.4, 2.5), and (.9, 2.5) is 3; in the top half of the parabola, the domain is limited to the range of -1 to -1/2, and in the bottom half, the domain is limited to the range of -1to -4/5.

Slope of asymptotes: 1 and -1.

-((y-2.5)/√(2.75))^2+((x-3)/√(2.75))^2=1

The set of points in a plane for each point of which the difference of the distances from the fixed points (-.89, 2.5), and (6.89, 2.5) is 3.32; in the top half of the parabola, the domain is limited to the range of 0 to 2, and in the bottom half, the domain is limited to the range of 1.1to 2.

Slope of asymptotes: 1 and -1.

-((y-2.5)/√(.75))^2+((x-1)/√(.75))^2=1

The set of points in a plane for each point of which the difference of the distances from the fixed points (-.06, 2.5), and (2.06, 2.5) is 1.73; in the top half of the parabola, the domain is limited to the range of 1 to 2.7, and in the bottom half, the domain is limited to the range of 1to 2.15.

Slope of asymptotes: 1 and -1.