**Correct option ****(c) α/x + β/y = 1**

**Explanation :**

See Fig .

Let the line AB be

x/a + y/b = 1

where A = (a, 0) and B = (0, b). This line passes through P (α,β) which implies that

α/a + β/b = 1 ...(1)

Let C(h, k) be the fourth vertex. Therefore, h = a and k = b. Hence, from Eq. (1), we have

α/h + β/k = 1

Therefore, the locus of C is

α/x + β/y = 1