Find the equation of the parabola with vertex at the origin, the axis

1.	Find the equation of the parabola with vertex at the origin, the axis along the Y-axis, and passing through the point (-10, -5).
Answer» Vertex of the parabola is at origin (0, 0) and its axis is along Y-axis. Equation of the parabola can be either x = 4by or x² = -4by Since the parabola passes through (-10, -5), it lies in 3rd quadrant. Required parabola is x² = -4by. Substituting x = -10 and y = -5 in x² = -4by, we get ⇒ (-10)² = -4b(-5) ⇒ b = 100/5 = 5 ∴ The required equation of the parabola is x² = -4(5)y, i.e., x² = -20y.

Find the equation of the parabola with vertex at the origin, the axis along the Y-axis, and passing through the point (-10, -5).

Answer»

Vertex of the parabola is at origin (0, 0) and its axis is along Y-axis.

Equation of the parabola can be either x = 4by or x² = -4by

Since the parabola passes through (-10, -5), it lies in 3rd quadrant.

Required parabola is x² = -4by.

Substituting x = -10 and y = -5 in x² = -4by, we get

⇒ (-10)² = -4b(-5)

⇒ b = 100/5 = 5

∴ The required equation of the parabola is x² = -4(5)y, i.e., x² = -20y.