1. a) Find the standard equation in rectangular coordinates of a conic section that has focus (1,-3) and directrix x=7

what conic has a single focus and directrix? its vertex is at (4,-3)
b) What is the standard equation of this conic section in polar coordinates if the coordinate system is taken with the pole at the focus?

2) a) convert 9x^2-4y^2+36x+24y-36=0 into its standard rectangular form.

this should get you started ...
b) What are the coordinates of the vertices?

c) What are the coordinates of the foci?

d) What is the eccentricity

e) What is the equation of the conic section in polar coordinates, if the pole is taken to be the leftmost focus?