The distance between the two points is 5 (given).
If the points given are endpoints, neither can be (-8,3), because one endpoint has a y value of 4 and 4 is not equal to 3; the other endpoint would make 2a=-8, a=-4 and the y coord would be -4-7=-11, which is not equal to 3.
If the given point was (8,-3), a=4 would fit and the other endpoint would be (6,4). The distance between them would be sqrt(7^2+2^2)=sqrt(53) which is not 5 as given.
The distance between the points in terms of a is sqrt((a-11)^2+(a-2)^2)=sqrt(a^2-22a+121+a^2-4a+4)=5.
2a^2-26a+125=25; 2a^2-26a+100=0; a^2-13a+50=0, which has no real roots.
Clearly from several points of view this question has been misstated.