For a curve at which the tangent lines at two distinct points coincide, then the

For a quadratic curve y = ax^2 + bx + c, the derivative dy/dx = 2ax + b is a linear function, which is strictly monotonic if a ≠ 0. Therefore, no two distinct points have the same slope, making coincident tangents impossible. In contrast, a quartic curve (e.g., y = (x^2-1)^2) can have the same tangent at two distinct points. A cubic curve also cannot have coincident tangents because the degree is too low for a line to be tangent at two distinct points. Hence, the curve cannot be a quadratic curve.