1. Given the parabola defined by y^2 = -12x, find the coordinates of the focus, the length of the latus rectum and the coordinates of its endpoints. Find also the equation of the dielectric. Sketch the graph.

Question

2. Find the eccentricity of an ellipse when the length of the latus rectum is 2/3 of the length of the major axis.

Answer 1

y^2 = 4px
has directrix x = -p
focus x = p
the l.r. has length 2p.
No electricity is involved.

the l.r. of an ellipse has length 2b^2/a

recall that b^2+c^2 = a^2
and eccentricity is c/a