p143 q9 c

I have problem in (c). I get the answer 2x+y = 0 but the book says it is 2x+3y = 0

question:

consider an ellipse E:

and a line L :

**I assume that you mean: 2x-3y+6=0**
and D:

is a line parallel to L.

a) if D cuts E at

and

, show that

and

are the roots of the equation

b) find the range of values of c if E and D cut at (i) 2 points / (ii) 1 point

c) M is the mid - point of QR. Find the equation of the locus M as c varies.

here's my working in (c)

2x+y = 0

but answer says it's 2x+3y=0. what's wrong??? thanks!