Geometric Series and the intersection of two graphs.

Questions:

1. How many solutions (x,y) are there for the system of equations:

$\displaystyle \displaystyle x^2+y^2+3x-14y+30=0$

$\displaystyle \displaystyle y^2-7xy+10x^2=0$

2. In a geometric series of positive terms, each term is the sum of the two following terms. What is the common ratio?

Both of these questions are meant to be done without calculators.

I have no clue where to start on number 1. On number 2, I tried setting up a system of equations, but fell one equation short:

let a,b, and c be three consecutive terms of the series.

a=b+c

and

c/b = b/a

are the two equations I came up with, but they are not enough to solve the system.

Any help is appreciated!