Precal Help?

Question

Graph the conic section. 

r = 12/ (10 + 5 sin θ) 


Specify the center, the eccentricity, and the lengths of the major and minor axes. 

center (x, y) = 
eccentricity =
length of major axis=
length of minor axis =

Answer 1

To change the expression (y ² + (120/75)y) into a perfect square trinomial,

 add (half the y coefficient)² to each side of the equation.

Answer 2

Compare it to standard form of vertical ellipse

Length of major axis 2a = 3.2

Length of minor axis 2b = 2.76

Eccentricity

The points for this ellipse are ,

Right most point (h +b , k )

Left most point (h - b , k )

Top most point (h , k + a )

Bottom most point (h , k - a )

Right most point (1.38, -4/5)

Left most point (-1.38, -4/5)

Top most point (0,0.8)

Bottom most point (0, -2.4)

Graph

1. draw the coordinate plane.

2. Plot the center at (0, -4/5).

3.Plot 4 points away from the center in the up, down, left and right direction.

4.Sketch the ellipse.