(1) B 2-4ac = 0 because there is only one intersection.
Because b+ac=3, AC = 3-B.
(b-2) (b+6) of simultaneous expression = 0.
B=2 or b=-6.
Because the parabola axis of symmetry is -b/2a, it can be seen from the figure that this value is greater than 0.
And because a<0 (open down)
So b=2.
(2)p(- 1/a,0),q(0,c)
Principle of triangle area equality (-1/a)*(-c)=pq*oa
Where pq can be calculated from the p and q coordinates,
The above formula can be simplified as 2+2 (AC) 2 = c 2.
Ac= 1 from b 2-4ac = 0.
So c=-2
So a=- 1/2.
I hope it will be helpful and adopted.