Final answer:
The locus of a point with coordinates (a,b) corresponding to a quadratic equation with equal roots is a parabola, given the condition that the discriminant b² - 4ac is zero.
Step-by-step explanation:
The student has inquired about the locus of a point (a,b) given a quadratic equation in x with a and b as parameters, where the equation has equal roots. For a quadratic equation of the form ax² + bx + c = 0, equal roots occur when the discriminant (b² - 4ac) is equal to zero.
Since the student's question does not include a term c, we shall assume c to be a constant, not a variable. Given this, the locus of point (a, b) when the discriminant is zero can be represented as b² = 4ac, which upon replacing c with a constant and solving for b, represents a parabola.
If we take c as a constant value, then we are basically looking for values of a and b that satisfy the condition b² = 4ac, with a not equal to zero. Therefore, the correct answer is (c) A parabola.