3:4
4:5
5:8
2:3
Equation of tangent at M is: x/32 + y√68 = 1
Let us put y=0 as the intersection will be on X-axis.
∴R=(6,0)
Equation of normal at m is: √32x + y = 2√32 + (√32)³
Putting y=0, we get: x = 2 + 32 = 72
∴Q=(72,0)
∴Area (ΔMQR) = 1/2 × (6 - 0) × √6 = 54√6 sq. unit
Area of quadrilateral (MF1NF2) = 2 × Area (ΔF1F2M) = 2 × 1/2 × 2 × √6 = 2√6 sq. unit
∴required ratio = 54/2 = 58