Step 1: Understanding the Question:
The smear shows target cells, nucleated red cells, and a microcytic hypochromic anemia, and there is a positive family history. We need to pick the test that will confirm the diagnosis.
Step 2: Key Concept:
This exact combination, target cells plus nucleated RBCs plus microcytic hypochromic anemia plus a family history, is the classic picture of an inherited hemoglobin disorder, most often thalassemia. Nucleated RBCs and target cells appear because the bone marrow is under stress trying to compensate for ineffective red cell production.
Step 3: Detailed Explanation:
Hb electrophoresis separates the different hemoglobin types (HbA, HbA2, HbF) by their electrical charge and directly shows the abnormal pattern seen in thalassemia, such as a raised HbA2 or HbF. This makes the diagnosis certain, so it is the investigation of choice.
Coombs test looks for antibody coating on red cells and is used to diagnose autoimmune hemolytic anemia, which is not suggested by a family history or this smear pattern.
Osmotic fragility testing checks how easily red cells burst in dilute saline. In thalassemia the fragility is actually decreased because target cells resist lysis, but this test is a rough screening tool, not specific enough to confirm the diagnosis.
Sucrose lysis test is used to screen for paroxysmal nocturnal hemoglobinuria, an acquired disorder unrelated to this inherited picture.
Step 4: Final Answer:
Hb electrophoresis is the test that confirms the diagnosis here.