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Question
Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)
Solution
Given equation of the parabola is (y - 2)2 = 4(x - 1)
⇒ y2 = 4X where X = x - 1 and Y = y - 2
⇒ 4a = 4
⇒ a = 1
| Referred to (X, Y) |
Referred to (x, y) x = X + 1, Y = y + 2 |
|
| Axis | X-axis ⇒ Y = 0 |
y - 2 = 0 ⇒ y = 2 |
| Vertex | (0, 0) | (1, 2) |
| Focus (0, 0) | (1, 0) | (2, 2) |
| Equation of directrix | X = - a ⇒ X = - 1 |
x - 1 = - 1 ⇒ x = 0 |
| Length of latus rectum |
4a = 4 | 4 |
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