29. x = at² ; y = 2at is the parametric equation of ? a. Parabola b. Circle c. Rectangular hyperbola d. Ellipse
Conic Sections: The general equations of various conic sections are: Straight Line: ax + by = c. Parabola: y2 = 4ax OR x2 = 4ay. Circle: x2 + y2 = r2. Ellipse: . Hyperbola: . Rectangular Hyperbola: xy = k. Calculation: Consider the given parametric form (at2, 2at). Here, x = at2 and y = 2at. It can be observed that y2 = 4a2t2 and 4ax = 4a(at2) = 4a2t2. Since y2 = 4ax, the given parametric form of the curve represents a parabola of the type y2 = 4ax.
