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Question
Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x2 – 2x + 3
Solution
The equation of the parabola is x2 – 2x + 3 = y
∴ x2 – 2x + 1 = y – 2
∴ (x – 1)2 = y – 2
Comparing with X2 = 4bY, we get
X = x – 1, Y = y – 2, 4b = 1
∴ b = `1/4`
Coordinates of the focus are given by
X = 0, Y = b
∴ x – 1 = 0, y – 2 = `1/4`
∴ x = 1, y = `9/4`
∴ focus = `(1, 9/4)`
Coordinates of the vertex are X = 0, Y = 0
∴ x – 1 = 0, y – 2 = 0
∴ x = 1, y = 2
∴ vertex = (1, 2)
Equation of directrix is
Y + b = 0
∴ `y - 2 + 1/4` = 0
∴ 4y – 7 = 0
Equation of axis is X = 0
∴ x – 1 = 0, i.e., x = 1.
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