Question

The vertex of a parabola is the point (a, b) and latus–rectum is of length l. If the axis of the parabola is along the positive direction of the y-axis then its equation is

• A. (x + a)² = (2y – 2b)
• B. (x – a)² = (2y – 2b)
• C. (x + a)² = $\frac { 1 } { 4 }$(2y – 2b)
• D. (x – a)² = (2y – 2b)

Answer 1

Answer: (B)

(x – a)² = (2y – 2b)

Answer 2

The equation of the parabola referred to its vertex as the origin is X² = lY, where x = X + a, y = Y +b. Therefore the equation of the parabola referred to the point (a, b) as the vertex is (x – a)² = l(y – b) or (x – a)² = $\frac { 1 } { 2 }$ (2y – 2b).