First we check which point satisfy the equation of hyperbola. All points in options are satisfied the equation of hyperbola 3x2−4y2=72. Now, we find one-by-one the length of perpendicular from point on Ellipse to the line 3x+2y+1=0 P(−6,3)=
11
√13
P(6,3)=
25
√13
P(−6,−3)=
23
√13
P(6,−3)=
13
√13
P(√24,0)=
3√24+1
√13
The minimum length is P(−6,3). So, the point (−6,3) is nearest to the given line.